Honorary Associate Professor

Dr Mike Hirschhorn

Science
Sch of Mathematics & Statistic
Phone
9385 7093
Location
School of Mathematics and Statistics UNSW Sydney NSW 2052 The Red Centre Room 6109

Publications

  • Book Chapters | 2021
    Dr Mike Hirschhorn
    Chern S; Hirschhorn MD, 2021, 'Partitions into Distinct Parts Modulo Powers of 5', in Trends in Mathematics, pp. 305 - 328, http://dx.doi.org/10.1007/978-3-030-57050-7_17
    Book Chapters | 2017
    Dr Mike Hirschhorn
    Hirschhorn MD, 2017, 'Introduction', in Developments in Mathematics, pp. 1 - 17, http://dx.doi.org/10.1007/978-3-319-57762-3_1
    Books | 2017
    Dr Mike Hirschhorn
    Hirschhorn MD, 2017, The Power of q A Personal Journey, Springer
  • Journal articles | 2021
    Dr Mike Hirschhorn
    Chern S; Hirschhorn MD, 2021, 'Some results concerning partitions with designated summands', Ramanujan Journal, vol. 54, pp. 385 - 395, http://dx.doi.org/10.1007/s11139-019-00198-1
    Journal articles | 2020
    Dr Mike Hirschhorn
    Hirschhorn MD, 2020, 'Cubic partitions modulo powers of 5', Ramanujan Journal, vol. 51, pp. 67 - 84, http://dx.doi.org/10.1007/s11139-018-0074-z
    Journal articles | 2020
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2020, 'Congruences for overpartitions with restricted odd differences', Ramanujan Journal, vol. 53, pp. 167 - 180, http://dx.doi.org/10.1007/s11139-019-00156-x
    Journal articles | 2019
    Dr Mike Hirschhorn
    Hirschhorn MD, 2019, 'Two remarkable q-series expansions', Ramanujan Journal, vol. 49, pp. 451 - 463, http://dx.doi.org/10.1007/s11139-018-0016-9
    Journal articles | 2019
    Dr Mike Hirschhorn
    Chern S; Hirschhorn MD, 2019, 'Partitions into Distinct Parts Modulo Powers of 5', Annals of Combinatorics, vol. 23, pp. 659 - 682, http://dx.doi.org/10.1007/s00026-019-00439-6
    Journal articles | 2019
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2019, 'PARITY RESULTS for PARTITIONS WHEREIN EACH PART APPEARS AN ODD NUMBER of TIMES', Bulletin of the Australian Mathematical Society, vol. 99, pp. 51 - 55, http://dx.doi.org/10.1017/S0004972718001041
    Journal articles | 2018
    Dr Mike Hirschhorn
    Hirschhorn MD, 2018, 'A conjecture of B. Lin on cubic partition pairs', Ramanujan Journal, vol. 45, pp. 781 - 795, http://dx.doi.org/10.1007/s11139-017-9926-1
    Journal articles | 2018
    Dr Mike Hirschhorn
    Hirschhorn MD, 2018, 'Partitions in 3 colours', Ramanujan Journal, vol. 45, pp. 399 - 411, http://dx.doi.org/10.1007/s11139-016-9835-8
    Journal articles | 2018
    Dr Mike Hirschhorn
    Hirschhorn MD, 2018, 'Broken 2-diamond partitions modulo 5', Ramanujan Journal, vol. 45, pp. 517 - 520, http://dx.doi.org/10.1007/s11139-016-9863-4
    Journal articles | 2018
    Dr Mike Hirschhorn
    Hirschhorn MD, 2018, 'Congruences modulo 5 for partitions into at most four parts', Fibonacci Quarterly, vol. 56, pp. 32 - 37
    Journal articles | 2017
    Dr Mike Hirschhorn
    Gireesh DS; Hirschhorn MD; Naika MSM, 2017, 'On 3-regular partitions with odd parts distinct', Ramanujan Journal, vol. 44, pp. 227 - 236, http://dx.doi.org/10.1007/s11139-016-9814-0
    Journal articles | 2017
    Dr Mike Hirschhorn
    Hirschhorn MD, 2017, 'Partitions and powers of 13', Journal of Number Theory, vol. 178, pp. 146 - 157, http://dx.doi.org/10.1016/j.jnt.2017.02.016
    Journal articles | 2016
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2016, 'Infinitely many congruences modulo 5 for 4-colored Frobenius partitions', Ramanujan Journal, vol. 40, pp. 193 - 200, http://dx.doi.org/10.1007/s11139-014-9652-x
    Journal articles | 2016
    Dr Mike Hirschhorn
    Hirschhorn MD, 2016, 'Some congruences for 6-colored generalized Frobenius partitions', Ramanujan Journal, vol. 40, pp. 463 - 471, http://dx.doi.org/10.1007/s11139-015-9700-1
    Journal articles | 2016
    Dr Mike Hirschhorn
    Hirschhorn MD, 2016, 'On the 2- and 4-dissections of the Rogers–Ramanujan functions', Ramanujan Journal, vol. 40, pp. 227 - 235, http://dx.doi.org/10.1007/s11139-014-9657-5
    Journal articles | 2015
    Dr Mike Hirschhorn
    Chen SC; Hirschhorn MD; Sellers JA, 2015, 'Arithmetic properties of Andrews' singular overpartitions', International Journal of Number Theory, vol. 11, pp. 1463 - 1476, http://dx.doi.org/10.1142/S1793042115400011
    Journal articles | 2015
    Dr Mike Hirschhorn
    Hirschhorn MD, 2015, 'Some interesting q-series identities', Ramanujan Journal, vol. 36, pp. 297 - 304, http://dx.doi.org/10.1007/s11139-014-9646-8
    Journal articles | 2015
    Dr Mike Hirschhorn
    Hirschhorn MD, 2015, 'Elementary analysis in Ramanujan’s lost notebook', Ramanujan Journal, vol. 37, pp. 641 - 651, http://dx.doi.org/10.1007/s11139-013-9551-6
    Journal articles | 2015
    Dr Mike Hirschhorn
    Eichhorn DA; Hirschhorn MD, 2015, 'Notes on the spt function of George E. Andrews', Ramanujan Journal, vol. 38, pp. 17 - 34, http://dx.doi.org/10.1007/s11139-013-9554-3
    Journal articles | 2015
    Dr Mike Hirschhorn
    Hirschhorn MD; Toh PC, 2015, 'On a certain vector crank modulo 7', Electronic Journal of Combinatorics, vol. 22, http://dx.doi.org/10.37236/4316
    Journal articles | 2015
    Dr Mike Hirschhorn
    Hirschhorn MD, 2015, 'A connection between π and Φ', The Fibonacci Quarterly, vol. 53, pp. 42 - 47, http://www.fq.math.ca/53-1.html
    Journal articles | 2015
    Dr Mike Hirschhorn
    Hirschhorn MD, 2015, 'Ramanujan’s Last Problem', The Fibonacci Quarterly, vol. 53, pp. 48 - 52
    Journal articles | 2015
    Dr Mike Hirschhorn
    Hirschhorn MD, 2015, 'Binomial identities and congruences for Euler numbers', Fibonacci Quarterly, vol. 53, pp. 319 - 322
    Journal articles | 2014
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2014, 'Arithmetic properties of 1-shell totally symmetric plane partitions', Bulletin of the Australian Mathematical Society, vol. 89, pp. 473 - 478
    Journal articles | 2014
    Dr Mike Hirschhorn
    Hirschhorn MD; Villarino MB, 2014, 'A refinement of Ramanujan's factorial approximation', Ramanujan Journal, vol. 34, pp. 73 - 81, http://dx.doi.org/10.1007/s11139-013-9494-y
    Journal articles | 2014
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2014, 'A congruence modulo 3 for partitions into distinct non-multiples of four', Journal of Integer Sequences, vol. 17
    Journal articles | 2014
    Dr Mike Hirschhorn
    Hirschhorn MD, 2014, 'A short and simple proof of Ramanujan's mod 11 partition congruence', Journal of Number Theory, vol. 139, pp. 205 - 209, http://dx.doi.org/10.1016/j.jnt.2013.12.014
    Journal articles | 2014
    Dr Mike Hirschhorn
    Hirschhorn MD, 2014, 'Stirling without Wallis', Fibonacci Quarterly, vol. 52, pp. 321 - 324
    Journal articles | 2014
    Dr Mike Hirschhorn
    Hirschhorn MD, 2014, 'The number of different parts in the partitions of n', Fibonacci Quarterly, vol. 52, pp. 10 - 15
    Journal articles | 2013
    Dr Mike Hirschhorn
    Hirschhorn MD, 2013, 'Factorizations of certain q-series identities of Ramanujan and others', Ramanujan Journal, vol. 31, pp. 15 - 22, http://dx.doi.org/10.1007/s11139-012-9419-1
    Journal articles | 2013
    Dr Mike Hirschhorn
    Hirschhorn MD, 2013, 'The asymptotic behavior of \prod_{k=1}^n\binom{n,k}', Fibonacci Quarterly, vol. 51, pp. 163 - 173
    Journal articles | 2013
    Dr Mike Hirschhorn
    Hirschhorn MD, 2013, 'A constant in a formula of Ramanujan', Mathematical Gazette, vol. 97, pp. 276, http://dx.doi.org/10.1017/S0025557200005921
    Journal articles | 2013
    Dr Mike Hirschhorn
    Hirschhorn MD, 2013, 'Estimating the apery numbers II', Fibonacci Quarterly, vol. 51, pp. 215 - 217
    Journal articles | 2013
    Dr Mike Hirschhorn
    Hirschhorn MD; Sinescu V, 2013, 'Elementary Algebra in Ramanujan’s Lost Notebook', Fibonacci Quarterly, vol. 51, pp. 123 - 129, http://web.maths.unsw.edu.au/~mikeh/webpapers/paper187.pdf
    Journal articles | 2013
    Dr Mike Hirschhorn
    Hirschhorn MD, 2013, 'The number of 1's in the partitions of n', Fibonacci Quarterly, vol. 51, pp. 326 - 329
    Journal articles | 2013
    Dr Mike Hirschhorn
    Journal articles | 2013
    Dr Mike Hirschhorn
    Journal articles | 2013
    Dr Mike Hirschhorn
    Hirschhorn MD; Villarino MB, 2013, 'A naive proof that F5n ≡ 0 (mod 5)', Fibonacci Quarterly, vol. 51, pp. 256 - 258
    Journal articles | 2013
    Dr Mike Hirschhorn
    Hirschhorn MD, 2013, 'A sequence considered by Shaun Cooper', New Zealand Journal of Mathematics (Online), vol. 43, pp. 31 - 36, http://web.maths.unsw.edu.au/~mikeh/webpapers/paper183.pdf
    Journal articles | 2012
    Dr Mike Hirschhorn
    Hirschhorn MD, 2012, 'Ramanujan's enigmatic formula for the harmonic series', Ramanujan Journal, vol. 27, pp. 343 - 347, http://dx.doi.org/10.1007/s11139-011-9322-1
    Journal articles | 2012
    Dr Mike Hirschhorn
    Hirschhorn MD, 2012, '“Algebraical oddities” in Ramanujan’s lost notebook', Ramanujan Journal, vol. 29, pp. 69 - 77, http://dx.doi.org/10.1007/s11139-012-9395-5
    Journal articles | 2012
    Dr Mike Hirschhorn
    Hirschhorn MD, 2012, 'Inequalities for Euler's constant', Mathematical Gazette, vol. 96, pp. 133 - 136, http://dx.doi.org/10.1017/S0025557200004174
    Journal articles | 2012
    Dr Mike Hirschhorn
    Hirschhorn MD, 2012, 'The number of sequences of n tosses of a coin with k pairs of consecutive heads', Fibonacci Quarterly, vol. 50, pp. 140 - 143
    Journal articles | 2012
    Dr Mike Hirschhorn
    Hirschhorn MD, 2012, 'Estimating the Apery numbers', Fibonacci Quarterly, vol. 50, pp. 129 - 131
    Journal articles | 2012
    Dr Mike Hirschhorn
    Hirschhorn MD, 2012, 'A note on overcubic partitions', New Zealand Journal of Mathematics (Online), vol. 42, pp. 229 - 234, http://web.maths.unsw.edu.au/~mikeh/webpapers/paper181.pdf
    Journal articles | 2011
    Dr Mike Hirschhorn
    Hirschhorn MD, 2011, 'An interesting integral', MATHEMATICAL GAZETTE, vol. 95, pp. 90 - 91, http://dx.doi.org/10.1017/S0025557200002436
    Journal articles | 2011
    Dr Mike Hirschhorn
    Cooper S; Hirschhorn MD, 2011, 'Factorizations that involve Ramanujan’s function k(q) = r(q)r 2(q 2)', ACTA Mathematica Sinica - English Series, vol. 27, pp. 2301 - 2318, http://dx.doi.org/10.1007/s10114-011-0202-9
    Journal articles | 2011
    Dr Mike Hirschhorn
    Hirschhorn MD, 2011, 'A note on Somos' quadratic recurrence constant', Journal of Number Theory, vol. 131, pp. 2061 - 2063, http://dx.doi.org/10.1016/j.jnt.2011.04.010
    Journal articles | 2011
    Dr Mike Hirschhorn
    Hirschhorn MD, 2011, 'Ramanujan's "most beautiful identity"', American Mathematical Monthly, vol. 118, pp. 839 - 845, http://dx.doi.org/10.4169/amer.math.monthly.118.09.839
    Journal articles | 2011
    Dr Mike Hirschhorn
    Hirschhorn MD, 2011, 'On the 2- and 4-dissections of Ramanujan's continued fraction and its reciprocal', Ramanujan Journal, vol. 24, pp. 85 - 92, http://dx.doi.org/10.1007/s11139-010-9272-z
    Journal articles | 2011
    Dr Mike Hirschhorn
    Hirschhorn MD, 2011, 'A simple proof that zeta(2) = pi2/6', Mathematical Intelligencer, vol. 33, pp. 81 - 82, http://dx.doi.org/10.1007/s00283-011-9217-4
    Journal articles | 2011
    Dr Mike Hirschhorn
    Hirschhorn MD, 2011, 'Tenth order algorithms for calculating root 2, (sic)', MATHEMATICAL GAZETTE, vol. 95, pp. 526 - 528, http://dx.doi.org/10.1017/S0025557200003697
    Journal articles | 2011
    Dr Mike Hirschhorn
    Hirschhorn M, 2011, '95.40 Lord Brouncker's continued fraction for pi', MATHEMATICAL GAZETTE, vol. 95, pp. 322 - 326, http://dx.doi.org/10.1017/S002555720000317X
    Journal articles | 2011
    Dr Mike Hirschhorn
    Hirschhorn MD, 2011, 'When is the sum of consecutive squares a square?', MATHEMATICAL GAZETTE, vol. 95, pp. 511 - 512, http://dx.doi.org/10.1017/S0025557200003636
    Journal articles | 2011
    Dr Mike Hirschhorn
    Hirschhorn MD, 2011, 'A triangle-folding problem', MATHEMATICAL GAZETTE, vol. 95, pp. 514 - 517, http://dx.doi.org/10.1017/S002555720000365X
    Journal articles | 2011
    Dr Mike Hirschhorn
    Hirschhorn M, 2011, '95.35 A surprising appearance of zeta(3)', MATHEMATICAL GAZETTE, vol. 95, pp. 313 - 313, http://dx.doi.org/10.1017/S0025557200003120
    Journal articles | 2011
    Dr Mike Hirschhorn
    Hirschhorn MD, 2011, 'Maximisation/minimisation without calculus', MATHEMATICAL GAZETTE, vol. 95, pp. 83 - 85, http://dx.doi.org/10.1017/S0025557200002400
    Journal articles | 2011
    Dr Mike Hirschhorn
    Hirschhorn MD, 2011, 'Commensurable triangles', MATHEMATICAL GAZETTE, vol. 95, pp. 61 - 63, http://dx.doi.org/10.1017/S0025557200002345
    Journal articles | 2011
    Dr Mike Hirschhorn
    Hirschhorn MD, 2011, 'Factorization of lens sequences', Fibonacci Quarterly, vol. 49, pp. 110 - 115, http://dx.doi.org/10.1007/s11139-010-9272-z
    Journal articles | 2011
    Dr Mike Hirschhorn
    Hirschhorn MD, 2011, 'A Simple Proof that ζ(2) = π2/6', Mathematical Intelligencer, vol. 33, pp. 81 - 82, http://dx.doi.org/10.1007/s00283-011-9217-4
    Journal articles | 2011
    Dr Mike Hirschhorn
    Hirschhorn MD, 2011, 'Approximating Euler's constant', Fibonacci Quarterly, vol. 49, pp. 243 - 248
    Journal articles | 2010
    Dr Mike Hirschhorn
    Andrews GE; Hirschhorn MD; Sellers JA, 2010, 'Arithmetic properties of partitions with even parts distinct', Ramanujan Journal, vol. 23, pp. 169 - 181, http://dx.doi.org/10.1007/s11139-009-9158-0
    Journal articles | 2010
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2010, 'Arithmetic properties of partitions with odd parts distinct', Ramanujan Journal, vol. 22, pp. 273 - 284, http://dx.doi.org/10.1007/s11139-010-9225-6
    Journal articles | 2010
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2010, 'Elementary proofs of parity results for 5–regular partitions', Bulletin of the Australian Mathematical Society, vol. 81, pp. 58 - 63, http://dx.doi.org/10.1017/S0004972709000525
    Journal articles | 2009
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2009, 'Elementary proofs of various facts about 3-cores', Bulletin of the Australian Mathematical Society, vol. 79, pp. 507 - 512, http://dx.doi.org/10.1017/S0004972709000136
    Journal articles | 2009
    Dr Mike Hirschhorn
    Hirschhorn MD, 2009, 'On recurrences of Fahr and Ringel arising in graph theory', Journal of Integer Sequences, vol. 12, pp. Article 09.6.8
    Journal articles | 2009
    Dr Mike Hirschhorn
    Hirschhorn MD, 2009, 'A problem involving binomial coefficients', Australian Mathematical Society Gazette, vol. 36, pp. 273 - 275
    Journal articles | 2009
    Dr Mike Hirschhorn
    Hirschhorn MD, 2009, 'Comment on 'Counting paths in a grid'', Australian Mathematical Society Gazette, vol. 36, pp. 50 - 52
    Journal articles | 2009
    Dr Mike Hirschhorn
    Hirschhorn MD; Rodseth OJ; Sellers JA, 2009, 'Infinite families of divisibility properties modulo 4 for non-squashing partitions into district parts', Integers, vol. 9, pp. 427 - 433
    Journal articles | 2008
    Dr Mike Hirschhorn
    Hirschhorn MD, 2008, 'A letter from Fitzroy house', American Mathematical Monthly, vol. 115, pp. 563 - 566
    Journal articles | 2008
    Dr Mike Hirschhorn
    Baruah ND; Cooper S; Hirschhorn MD, 2008, 'Sums of Squares and sums of triangular numbers induced by partitions of 8', International Journal of Number Theory, vol. 4, pp. 525 - 538, http://dx.doi.org/10.1142/S179304210800150X
    Journal articles | 2008
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2008, 'Enumeration of Unigraphical Partitions', Journal of Integer Sequences, vol. 2008
    Journal articles | 2008
    Dr Mike Hirschhorn
    Hirschhorn MD, 2008, 'Three scenarios involving elastic collisions', MATHEMATICAL GAZETTE, vol. 92, pp. 154 - 158, http://dx.doi.org/10.1017/S0025557200182816
    Journal articles | 2008
    Dr Mike Hirschhorn
    Hirschhorn MD, 2008, 'Pythagoras' Theorem', MATHEMATICAL GAZETTE, vol. 92, pp. 565 - 565, http://dx.doi.org/10.1017/S0025557200183950
    Journal articles | 2007
    Dr Mike Hirschhorn
    Cooper S; Hirschhorn MD, 2007, 'On the number of primitive representations of integers as sums of squares', Ramanujan Journal, vol. 13, pp. 7 - 25, http://dx.doi.org/10.1007/s11139-006-0240-6
    Journal articles | 2007
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2007, 'On recent congruence results of Andrews and Paule for broken k-diamonds', Bulletin of the Australian Mathematical Society, vol. 75, pp. 121 - 126
    Journal articles | 2007
    Dr Mike Hirschhorn
    Benjamin AT; Hirschhorn MD, 2007, 'A combinatorial solution to intertwined recurrences', Australasian Journal of Combinatorics, vol. 37, pp. 101 - 116
    Journal articles | 2007
    Dr Mike Hirschhorn
    Hirschhorn MD, 2007, 'Teaching Notes Teaching integration', MATHEMATICAL GAZETTE, vol. 91, pp. 547 - 547, http://dx.doi.org/10.1017/S0025557200182294
    Journal articles | 2007
    Dr Mike Hirschhorn
    Hirschhorn MD, 2007, 'Still shorter [2]', Mathematical Intelligencer, vol. 29, pp. 5, http://dx.doi.org/10.1007/BF02986196
    Journal articles | 2007
    Dr Mike Hirschhorn
    Hirschhorn MD, 2007, 'The AM-GM inequality', Mathematical Intelligencer, vol. 29, pp. 7 - 7, http://dx.doi.org/10.1007/BF02986168
    Journal articles | 2007
    Dr Mike Hirschhorn
    Hirschhorn MD, 2007, 'Correspondence', MATHEMATICAL GAZETTE, vol. 91, pp. 560 - 560, http://dx.doi.org/10.1017/S0025557200182348
    Journal articles | 2007
    Dr Mike Hirschhorn
    Hirschhorn MD, 2007, 'The alternating harmonic series', Mathematical Intelligencer, vol. 29, pp. 4 - 5
    Journal articles | 2006
    Dr Mike Hirschhorn
    Hirschhorn MD, 2006, '90.16 Evaluating (sic) (a', MATHEMATICAL GAZETTE, vol. 90, pp. 114 - 116, http://dx.doi.org/10.1017/S0025557200179197
    Journal articles | 2006
    Dr Mike Hirschhorn
    Cooper S; Hirschhorn M, 2006, 'Sums of squares and sums of triangular numbers', Georgian Mathematical Journal, vol. 13, pp. 675 - 686, http://dx.doi.org/10.1515/GMJ.2006.675
    Journal articles | 2006
    Dr Mike Hirschhorn
    Hirschhorn MD, 2006, 'The case of the mysterious sevens', International Journal of Number Theory, vol. 2, pp. 213 - 216
    Journal articles | 2006
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2006, 'Arithmetic properties of overpartitions into odd parts', Annals of Combinatorics, vol. 10, pp. 353 - 367, http://dx.doi.org/10.1007/s00026-006-0293-7
    Journal articles | 2006
    Dr Mike Hirschhorn
    Hirschhorn MD, 2006, '90.54 The new neighbours problem: a solution', MATHEMATICAL GAZETTE, vol. 90, pp. 321 - 324, http://dx.doi.org/10.1017/S0025557200179884
    Journal articles | 2006
    Dr Mike Hirschhorn
    Hirschhorn MD, 2006, '90.04 The number of partitions of a number into distinct squares', MATHEMATICAL GAZETTE, vol. 90, pp. 80 - 87, http://dx.doi.org/10.1017/S0025557200179070
    Journal articles | 2006
    Dr Mike Hirschhorn
    Hirschhorn MD, 2006, 'On Euler's constant', MATHEMATICAL GAZETTE, vol. 90, pp. 295 - 298, http://dx.doi.org/10.1017/S002555720017977X
    Journal articles | 2006
    Dr Mike Hirschhorn
    Hirschhorn MD, 2006, 'Coupled third-order recurrences', Fibonacci Quarterly, vol. 44, pp. 26 - 31
    Journal articles | 2006
    Dr Mike Hirschhorn
    Hirschhorn MD, 2006, 'Coupled second-order recurrences', Fibonacci Quarterly, vol. 44, pp. 20 - 25
    Journal articles | 2005
    Dr Mike Hirschhorn
    Angell DD; Hirschhorn MD, 2005, 'A remarkable continued fraction', Bulletin of the Australian Mathematical Society, vol. 72, pp. 45 - 52
    Journal articles | 2005
    Dr Mike Hirschhorn
    Hirschhorn MD, 2005, 'The number of representations of a number by various forms', Discrete Mathematics, vol. 298, pp. 205 - 211, http://dx.doi.org/10.1016/j.disc.2004.08.045
    Journal articles | 2005
    Dr Mike Hirschhorn
    Hirschhorn MD, 2005, 'An identity involving binomial coefficients', MATHEMATICAL GAZETTE, vol. 89, pp. 256 - 258, http://dx.doi.org/10.1017/S0025557200177745
    Journal articles | 2005
    Dr Mike Hirschhorn
    Doust IR; Hirschhorn MD; Ho J, 2005, 'Trigonometric identities, linear algebra, and computer algebra', American Mathematical Monthly, vol. 112, pp. 155 - 164, http://dx.doi.org/10.2307/30037413
    Journal articles | 2005
    Dr Mike Hirschhorn
    Hirschhorn MD, 2005, 'Non-trivial intertwined second-order recurrence relations', Fibonacci Quarterly, vol. 43, pp. 316 - 325
    Journal articles | 2005
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2005, 'Further results for partitions into four squares of equal parity', ARS Combinatoria, vol. 76, pp. 33 - 45
    Journal articles | 2005
    Dr Mike Hirschhorn
    Hirschhorn MD, 2005, 'Ramanujan`s `most beautiful identity`', Australian Mathematical Society Gazette, vol. 32, pp. 259 - 262
    Journal articles | 2005
    Dr Mike Hirschhorn
    Hirschhorn MD, 2005, 'On representations of pi and squareroot 2', Australian Mathematical Society Gazette, vol. 32, pp. 124 - 126
    Journal articles | 2005
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2005, 'An infinite family of overpartition congruences modulo 12', Integers: the Electronic Journal of Combinatorial Number Theory, vol. 5, pp. A20 - A20
    Journal articles | 2005
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2005, 'Arithmetic relations for overpartitions', Journal of Combinatorial Mathematics and Combinatorial Computing, vol. 53, pp. 65 - 73
    Journal articles | 2005
    Dr Mike Hirschhorn
    Cooper S; Gun S; Hirschhorn MD; Ramakrishnan B, 2005, 'Relations among Fourier coefficients of certain eta products', Integers: the Electronic Journal of Combinatorial Number Theory, vol. 5, pp. A16
    Journal articles | 2004
    Dr Mike Hirschhorn
    Cooper S; Hirschhorn MD, 2004, 'Results of Hurwitz type for three squares', Discrete Mathematics, vol. 274, pp. 9 - 24, http://dx.doi.org/10.1016/S0012-365X(03)00079-7
    Journal articles | 2004
    Dr Mike Hirschhorn
    Sheppard C; Campbell S; Hirschhorn MD, 2004, 'Zernike expansion of separable functions of Cartesian coordinates', Applied Optics, vol. 43, pp. 3963 - 3966, http://dx.doi.org/10.1364/AO.43.003963
    Journal articles | 2004
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2004, 'On a problem of Lehmer on partitions into squares', Ramanujan Journal, vol. 8, pp. 279 - 287, http://dx.doi.org/10.1007/s11139-004-0138-0
    Journal articles | 2004
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2004, 'Partitions into three triangular numbers', Australasian Journal of Combinatorics, vol. 30, pp. 307 - 318
    Journal articles | 2004
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2004, 'A different view of m-ary partitions', Australasian Journal of Combinatorics, vol. 30, pp. 193 - 196
    Journal articles | 2004
    Dr Mike Hirschhorn
    Cooper S; Hirschhorn MD, 2004, 'A combinatorial proof of a result from number theory', Integers: the Electronic Journal of Combinatorial Number Theory, vol. 4
    Journal articles | 2002
    Dr Mike Hirschhorn
    Barrucand P; Hirschhorn MD, 2002, 'Formulae asociated with 5, 7, 9 and 11 squares', Bulletin of the Australian Mathematical Society, vol. 65, pp. 503 - 510
    Journal articles | 2002
    Dr Mike Hirschhorn
    Barrucand P; Cooper S; Hirschhorn MD, 2002, 'Relations between squares and triangles', Discrete Mathematics, vol. 248, pp. 245 - 247, http://dx.doi.org/10.1016/S0012-365X(01)00344-2
    Journal articles | 2002
    Dr Mike Hirschhorn
    Barrucand P; Cooper S; Hirschhorn MD, 2002, 'Results of Hurwitz type for five or more squares', Ramanujan Journal, vol. 6, pp. 347 - 367, http://dx.doi.org/10.1023/A:1019753500261
    Journal articles | 2002
    Dr Mike Hirschhorn
    Hirschhorn MD, 2002, 'K-Gon partitions', Bulletin of the Australian Mathematical Society, vol. 66, pp. 149 - 150
    Journal articles | 2002
    Dr Mike Hirschhorn
    Hirschhorn MD, 2002, 'There are infinitely many prime numbers', Australian Mathematical Society Gazette, vol. 29, pp. 103 - 103
    Journal articles | 2002
    Dr Mike Hirschhorn
    Hirschhorn MD, 2002, 'Binomial coefficient identities and hyjpergeometric series', Australian Mathematical Society Gazette, vol. 29, pp. 203 - 208
    Journal articles | 2002
    Dr Mike Hirschhorn
    Hirschhorn MD, 2002, 'On sums of squares', Australian Mathematical Society Gazette, vol. 29, pp. 86 - 87
    Journal articles | 2002
    Dr Mike Hirschhorn
    Brown PG; Hirschhorn MD, 2002, 'A note on the Pell equation x2-(m2-4)y2 =1', Australian Mathematical Society Gazette, vol. 29, pp. 273 - 276
    Journal articles | 2001
    Dr Mike Hirschhorn
    Hirschhorn MD, 2001, 'On the expansion of a continued fraction of Gordon', Ramanujan Journal, vol. 5, pp. 369 - 375, http://dx.doi.org/10.1023/A:1013939720688
    Journal articles | 2001
    Dr Mike Hirschhorn
    Cooper S; Hirschhorn MD, 2001, 'On some infinite product identities', Rocky Mountain Journal of Mathematics, vol. 31, pp. 131 - 139, http://dx.doi.org/10.1216/rmjm/1008959672
    Journal articles | 2001
    Dr Mike Hirschhorn
    Cooper S; Hirschhorn MD, 2001, 'On some sum-to-product identities', Bulletin of the Australian Mathematical Society, vol. 63, pp. 353 - 365
    Journal articles | 2001
    Dr Mike Hirschhorn
    Hirschhorn MD, 2001, 'On partitions into four distinct squares of equal parity', Australasian Journal of Combinatorics, vol. 24, pp. 285 - 291
    Journal articles | 2000
    Dr Mike Hirschhorn
    Hirschhorn MD, 2000, 'Parity results for certain partition functions', Ramanujan Journal, vol. 4, pp. 129 - 135, http://dx.doi.org/10.1023/A:1009874919415
    Journal articles | 2000
    Dr Mike Hirschhorn
    Hirschhorn MD, 2000, 'Partial fractions and four classical theorems of number theory', American Mathematical Monthly, vol. 107, pp. 260 - 263, http://dx.doi.org/10.2307/2589321
    Journal articles | 2000
    Dr Mike Hirschhorn
    Cooper S; Hirschhorn MD; Lewis RA, 2000, 'Powers of Euler`s product and related identities', Ramanujan Journal, vol. 4, pp. 137 - 155, http://dx.doi.org/10.1023/A:1009827103485
    Journal articles | 2000
    Dr Mike Hirschhorn
    Hirschhorn MD, 2000, 'Arithmetic consequences of Jacobi`s two-squares theorem', Ramanujan Journal, vol. 4, pp. 51 - 57, http://dx.doi.org/10.1023/A:1009877906185
    Journal articles | 2000
    Dr Mike Hirschhorn
    Hirschhorn MD, 2000, 'More on Cootie', College Mathematics Journal, pp. 126 - 128
    Journal articles | 2000
    Dr Mike Hirschhorn
    Hirschhorn MD, 2000, 'Some formulae for partitions into squares', Discrete Mathematics, vol. 211, pp. 225 - 228, http://dx.doi.org/10.1016/S0012-365X(99)00159-4
    Journal articles | 2000
    Dr Mike Hirschhorn
    Hirschhorn MD, 2000, 'Winquist and the Atkin- Swinnerton-Dyer partition congruences for modulus 11', Australasian Journal of Combinatorics, vol. 22, pp. 101 - 104
    Journal articles | 2000
    Dr Mike Hirschhorn
    Hirschhorn MD, 2000, 'Triangles with integer sides, revisited', Mathematics Magazine, pp. 53 - 56
    Journal articles | 2000
    Dr Mike Hirschhorn
    Hirschhorn MD, 2000, 'How many ways can a king cross the board?', Australian Mathematical Society Gazette, pp. 104 - 106
    Journal articles | 2000
    Dr Mike Hirschhorn
    Hirschhorn MD, 2000, 'A proof of Eperson`s conjecture', Mathematical Gazette, pp. 442 - 446
    Journal articles | 2000
    Dr Mike Hirschhorn
    Hirschhorn MD, 2000, 'An identity of Ramanujan, and applications', Contemporary Mathematics, pp. 229 - 234
    Journal articles | 2000
    Dr Mike Hirschhorn
    Hirschhorn MD, 2000, 'Partiy results for certain partition functions', Ramanujan Journal, pp. 129 - 135
    Journal articles | 1999
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 1999, 'Some parity results for 16-cores', Ramanujan Journal, vol. 3, pp. 281 - 296, http://dx.doi.org/10.1023/A:1009879303577
    Journal articles | 1999
    Dr Mike Hirschhorn
    Hirschhorn MD, 1999, 'Basis partitions and Rogers-Ramanujan partitions', Discrete Mathematics, vol. 205, pp. 241 - 243, http://dx.doi.org/10.1016/S0012-365X(99)00030-8
    Journal articles | 1999
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 1999, 'On representations of a number as a sum of three squares', Discrete Mathematics, vol. 199, pp. 85 - 101
    Journal articles | 1999
    Dr Mike Hirschhorn
    Hirschhorn MD, 1999, 'Another short proof of Ramanujan`s mod 5 partition congruence, and more', American Mathematical Monthly, vol. 106, pp. 580 - 583
    Journal articles | 1999
    Dr Mike Hirschhorn
    Hirschhorn MD, 1999, 'Jacobi`s two-square theorem and related identities', Ramanujan Journal, vol. 3, pp. 153 - 158, http://dx.doi.org/10.1023/A:1006993323652
    Journal articles | 1999
    Dr Mike Hirschhorn
    Hirschhorn A; Hirschhorn MD; Hirschhorn P, 1999, 'The pizza theorem', Australian Mathematical Society Gazette, pp. 120 - 121
    Journal articles | 1999
    Dr Mike Hirschhorn
    Hirschhorn MD, 1999, 'A problem in dynamics', Australian Mathematical Society Gazette, pp. 34 - 41
    Journal articles | 1999
    Dr Mike Hirschhorn
    Hirschhorn MD, 1999, 'The double-angle formulae', Australian Mathematical Society Gazette, pp. 171 - 172
    Journal articles | 1998
    Dr Mike Hirschhorn
    Hirschhorn MD, 1998, 'On the expansion of Ramanujan`s continued fraction', Ramanujan Journal, vol. 2, pp. 521 - 527, http://dx.doi.org/10.1023/A:1009789012006
    Journal articles | 1998
    Dr Mike Hirschhorn
    Hirschhorn MD, 1998, 'Two or three identities of Ramanujan', American Mathematical Monthly, vol. 105, pp. 52 - 54, http://dx.doi.org/10.2307/2589526
    Journal articles | 1998
    Dr Mike Hirschhorn
    Hirschhorn MD, 1998, 'The fundamental theorem of algebra', College Mathematics Journal, pp. 276 - 277
    Journal articles | 1998
    Dr Mike Hirschhorn
    Hirschhorn MD, 1998, 'Proofs of some hyperelliptic function identities', Bulletin of the Australian Mathematical Society, vol. 58, pp. 465 - 468
    Journal articles | 1998
    Dr Mike Hirschhorn
    Hirschhorn MD, 1998, 'Two diophantine equations studied by Ramanujan', Mathematics Magazine, pp. 386 - 388
    Journal articles | 1998
    Dr Mike Hirschhorn
    Hirschhorn MD, 1998, 'Three classical results or representations of a number', Seminaire Lotharingien de Combinatoire, pp. 41
    Journal articles | 1998
    Dr Mike Hirschhorn
    Hirschhorn MD, 1998, 'A trigonometric identity and Morley`s theorem', Australian Mathematical Society Gazette, pp. 198 - 199
    Journal articles | 1998
    Dr Mike Hirschhorn
    Hirschhorn MD, 1998, 'The sum sqrt 1 + sqrt 2 + ¿ + sqrt n without integration', Australian Mathematical Society Gazette, pp. 143 - 145
    Journal articles | 1998
    Dr Mike Hirschhorn
    Hirschhorn MD, 1998, 'A new Formula for Pi', Australian Mathematical Society Gazette, pp. 82 - 83
    Journal articles | 1997
    Dr Mike Hirschhorn
    Hirschhorn MD, 1997, 'The volume of a cone, without calculus', Mathematics Magazine, pp. 295 - 296
    Journal articles | 1997
    Dr Mike Hirschhorn
    Hirschhorn MD, 1997, 'Radius of a buried pipe', Australian Mathematical Society Gazette, pp. 180 - 181
    Journal articles | 1996
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 1996, 'Two congruences involving 4-cores', Electronic Journal of Combinatorics, vol. 3, pp. 1 - 8
    Journal articles | 1996
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 1996, 'Some amazing facts about 4-cores', Journal of Number Theory, vol. 60, pp. 51 - 69, http://dx.doi.org/10.1006/jnth.1996.0112
    Journal articles | 1996
    Dr Mike Hirschhorn
    Hirschhorn MD, 1996, 'A reformulation of Ramanujan`s partition congruences', Journal of Combinatorial Theory Series A, vol. 73, pp. 346 - 347, http://dx.doi.org/10.1016/S0097-3165(96)80010-0
    Journal articles | 1996
    Dr Mike Hirschhorn
    Hirschhorn MD, 1996, 'Calkin`s binomial identity', Discrete Mathematics, vol. 159, pp. 273 - 278, http://dx.doi.org/10.1016/0012-365X(95)00086-C
    Journal articles | 1996
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 1996, 'On representations of a number as a sum of three triangles', ACTA Arithmetica, vol. 77, pp. 289 - 301, http://dx.doi.org/10.4064/aa-77-3-289-301
    Journal articles | 1996
    Dr Mike Hirschhorn
    Hirschhorn MD, 1996, 'A proof in the spirit of Zeilberger of an amazing identity of Ramanujan', Mathematics Magazine, pp. 267 - 269
    Journal articles | 1995
    Dr Mike Hirschhorn
    Hirschhorn MD, 1995, 'An amazing identity of Ramanujan', Mathematics Magazine, pp. 199 - 201
    Journal articles | 1995
    Dr Mike Hirschhorn
    Hirschhorn MD, 1995, 'A new proof of an old formula', Bulletin of the ICA, vol. 13, pp. 127
    Journal articles | 1994
    Dr Mike Hirschhorn
    Hirschhorn MD, 1994, 'Ramanujan's partition congruences', Discrete Mathematics, vol. 131, pp. 351 - 355, http://dx.doi.org/10.1016/0012-365X(94)90397-2
    Journal articles | 1994
    Dr Mike Hirschhorn
    Hirschhorn MD, 1994, 'Several Identities in Statistical Mechanics', International Journal of Mathematics and Mathematical Sciences, vol. 17, pp. 817 - 820, http://dx.doi.org/10.1155/S0161171294001146
    Journal articles | 1993
    Dr Mike Hirschhorn
    Hirschhorn MD, 1993, 'On the parity of p(n), II', Journal of Combinatorial Theory, Series A, vol. 62, pp. 128 - 138, http://dx.doi.org/10.1016/0097-3165(93)90075-J
    Journal articles | 1988
    Dr Mike Hirschhorn
    Hirschhorn MD, 1988, 'A generalisation of the quintuple product identity', Journal of the Australian Mathematical Society, vol. 44, pp. 42 - 45, http://dx.doi.org/10.1017/S1446788700031359
    Journal articles | 1987
    Dr Mike Hirschhorn
    Hirschhorn MD, 1987, 'A simple proof of Jacobi's four-square theorem', Proceedings of the American Mathematical Society, vol. 101, pp. 436 - 438, http://dx.doi.org/10.1090/S0002-9939-1987-0908644-9
    Journal articles | 1985
    Dr Mike Hirschhorn
    Hirschhorn MD; Hunt DC, 1985, 'Equilateral convex pentagons which tile the plane', Journal of Combinatorial Theory, Series A, vol. 39, pp. 1 - 18, http://dx.doi.org/10.1016/0097-3165(85)90078-0
    Journal articles | 1984
    Dr Mike Hirschhorn
    Guttmann AJ; Hirschhorn M, 1984, 'Comment on the number of spiral self-avoiding walks', Journal of Physics A: General Physics, vol. 17, pp. 3613 - 3614, http://dx.doi.org/10.1088/0305-4470/17/18/029
    Journal articles | 1983
    Dr Mike Hirschhorn
    Hirschhorn MD, 1983, 'A Simple proof of an identity of Ramanujan', Journal of the Australian Mathematical Society, vol. 34, pp. 31 - 35, http://dx.doi.org/10.1017/S1446788700019728
    Journal articles | 1982
    Dr Mike Hirschhorn
    Hirschhorn MD, 1982, 'A Simple Proof of Jacobi’s Four-Square Theorem', Journal of the Australian Mathematical Society, vol. 32, pp. 61 - 67, http://dx.doi.org/10.1017/S144678870002440X
    Journal articles | 1981
    Dr Mike Hirschhorn
    Hirschhorn MD, 1981, 'Infinitely many identities of kolberg type', Journal of the Australian Mathematical Society, vol. 31, pp. 20 - 25, http://dx.doi.org/10.1017/S1446788700018450
    Journal articles | 1981
    Dr Mike Hirschhorn
    Hirschhorn MD; Hunt DC, 1981, 'A simple proof of the Ramanujan conjecture for powers of 5', Journal fur die Reine und Angewandte Mathematik, vol. 1981, pp. 1 - 17, http://dx.doi.org/10.1515/crll.1981.326.1
    Journal articles | 1980
    Dr Mike Hirschhorn
    Hirschhorn MD, 1980, 'A continued fraction of ramanujan', Journal of the Australian Mathematical Society, vol. 29, pp. 80 - 86, http://dx.doi.org/10.1017/S1446788700020954
    Journal articles | 1980
    Dr Mike Hirschhorn
    Hirschhorn MD, 1980, 'Two further ramanujan pairs', Journal of the Australian Mathematical Society, vol. 30, pp. 1 - 4, http://dx.doi.org/10.1017/S1446788700021856
    Journal articles | 1979
    Dr Mike Hirschhorn
    Hirschhorn MD, 1979, 'Some partition theorems of the Rogers-Ramanujan type', Journal of Combinatorial Theory, Series A, vol. 27, pp. 33 - 37, http://dx.doi.org/10.1016/0097-3165(79)90005-0
    Journal articles | 1976
    Dr Mike Hirschhorn
    Hirschhorn MD, 1976, 'Simple proofs of identities of MacMahon and Jacobi', Discrete Mathematics, vol. 16, pp. 161 - 162, http://dx.doi.org/10.1016/0012-365X(76)90144-8
    Journal articles | 1975
    Dr Mike Hirschhorn
    Hirschhorn MD; Loxton JH, 1975, 'Congruence properties of the binary partition function', Mathematical Proceedings of the Cambridge Philosophical Society, vol. 78, pp. 437 - 442, http://dx.doi.org/10.1017/S0305004100051896
    Journal articles | 1974
    Dr Mike Hirschhorn
    Hirschhorn MD, 1974, 'A continued fraction', Duke Mathematical Journal, vol. 41, pp. 27 - 33, http://dx.doi.org/10.1215/S0012-7094-74-04104-0
    Journal articles | 1973
    Dr Mike Hirschhorn
    Hirschhorn MD, 1973, 'A continued fraction of Carlitz', Duke Mathematical Journal, vol. 40, pp. 77 - 80, http://dx.doi.org/10.1215/S0012-7094-73-04008-8
    Journal articles | 1972
    Dr Mike Hirschhorn
    Hirschhorn MD, 1972, 'Partitions and ramanujan’s continued fraction', Duke Mathematical Journal, vol. 39, pp. 789 - 791, http://dx.doi.org/10.1215/S0012-7094-72-03986-5
  • Conference Papers | 2016
    Dr Mike Hirschhorn
    Hirschhorn MD, 2016, 'Ramanujan’s tau function', in Springer Proceedings in Mathematics and Statistics, Gainesville, FL, USA, pp. 311 - 328, presented at Analytic Number Theory, Modular Forms and q-Hypergeometric Series, Gainesville, FL, USA, 17 March 2016 - 21 March 2016, http://dx.doi.org/10.1007/978-3-319-68376-8_18
    Conference Papers | 2001
    Dr Mike Hirschhorn
    Hirschhorn MD; Mcgowan JA, 2001, 'Algebraic consequences of Jacobi`s two- and four-square theorems', in Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, University of Florida, Gainesville, presented at Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, University of Florida, Gainesville, 11 November 1999 - 13 November 1999
    Conference Papers | 2000
    Dr Mike Hirschhorn
    Hirschhorn MD; Sellers JA, 2000, 'Some relations for partitions into four squares', in international workshop special functions, international workshop special functions, Hong Kong, presented at international workshop special functions, Hong Kong, 21 June 1999 - 25 June 1999

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