Hirschhorn MD, 2017, The Power of q A Personal Journey, Springer
Book Chapters | 2021
Chern S; Hirschhorn MD, 2021, 'Partitions into Distinct Parts Modulo Powers of 5', in George E. Andrews 80 Years of Combinatory Analysis, pp. 305 - 328, http://dx.doi.org/10.1007/978-3-030-57050-7_17
Hirschhorn MD; Sellers JA, 2019, 'PARITY RESULTS for PARTITIONS WHEREIN EACH PART APPEARS AN ODD NUMBER of TIMES', Bulletin of the Australian Mathematical Society, 99, pp. 51 - 55, http://dx.doi.org/10.1017/S0004972718001041
Chen SC; Hirschhorn MD; Sellers JA, 2015, 'Arithmetic properties of Andrews' singular overpartitions', International Journal of Number Theory, 11, pp. 1463 - 1476, http://dx.doi.org/10.1142/S1793042115400011
Hirschhorn MD; Sellers JA, 2014, 'A congruence modulo 3 for partitions into distinct non-multiples of four', Journal of Integer Sequences, 17
Journal articles | 2014
Hirschhorn MD; Sellers JA, 2014, 'Arithmetic properties of 1-shell totally symmetric plane partitions', Bulletin of the Australian Mathematical Society, 89, pp. 473 - 478
Hirschhorn MD, 2014, 'A short and simple proof of Ramanujan's mod 11 partition congruence', Journal of Number Theory, 139, pp. 205 - 209, http://dx.doi.org/10.1016/j.jnt.2013.12.014
Journal articles | 2014
Hirschhorn MD, 2014, 'Stirling without Wallis', Fibonacci Quarterly, 52, pp. 321 - 324
Journal articles | 2014
Hirschhorn MD, 2014, 'The number of different parts in the partitions of n', Fibonacci Quarterly, 52, pp. 10 - 15
Hirschhorn MD, 2013, 'Estimating the apery numbers II', Fibonacci Quarterly, 51, pp. 215 - 217
Journal articles | 2013
Hirschhorn MD, 2013, 'Factorizations of certain q-series identities of Ramanujan and others', Ramanujan Journal, 31, pp. 15 - 22, http://dx.doi.org/10.1007/s11139-012-9419-1
Hirschhorn MD, 2011, 'On the 2- and 4-dissections of Ramanujan's continued fraction and its reciprocal', Ramanujan Journal, 24, pp. 85 - 92, http://dx.doi.org/10.1007/s11139-010-9272-z
Andrews GE; Hirschhorn MD; Sellers JA, 2010, 'Arithmetic properties of partitions with even parts distinct', Ramanujan Journal, 23, pp. 169 - 181, http://dx.doi.org/10.1007/s11139-009-9158-0
Journal articles | 2010
Hirschhorn MD; Sellers JA, 2010, 'Arithmetic properties of partitions with odd parts distinct', Ramanujan Journal, 22, pp. 273 - 284, http://dx.doi.org/10.1007/s11139-010-9225-6
Journal articles | 2010
Hirschhorn MD; Sellers JA, 2010, 'Elementary proofs of parity results for 5–regular partitions', Bulletin of the Australian Mathematical Society, 81, pp. 58 - 63, http://dx.doi.org/10.1017/S0004972709000525
Journal articles | 2009
Hirschhorn MD; Rodseth OJ; Sellers JA, 2009, 'Infinite families of divisibility properties modulo 4 for non-squashing partitions into district parts', Integers, 9, pp. 427 - 433
Journal articles | 2009
Hirschhorn MD; Sellers JA, 2009, 'Elementary proofs of various facts about 3-cores', Bulletin of the Australian Mathematical Society, 79, pp. 507 - 512, http://dx.doi.org/10.1017/S0004972709000136
Journal articles | 2009
Hirschhorn MD, 2009, 'A problem involving binomial coefficients', Australian Mathematical Society Gazette, 36, pp. 273 - 275
Journal articles | 2009
Hirschhorn MD, 2009, 'Comment on 'Counting paths in a grid'', Australian Mathematical Society Gazette, 36, pp. 50 - 52
Journal articles | 2009
Hirschhorn MD, 2009, 'On recurrences of Fahr and Ringel arising in graph theory', Journal of Integer Sequences, 12, pp. Article 09.6.8
Journal articles | 2008
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, 4, pp. 525 - 538, http://dx.doi.org/10.1142/S179304210800150X
Journal articles | 2008
Hirschhorn MD; Sellers JA, 2008, 'Enumeration of Unigraphical Partitions', Journal of Integer Sequences, 2008
Journal articles | 2008
Hirschhorn MD, 2008, 'A letter from Fitzroy house', American Mathematical Monthly, 115, pp. 563 - 566
Benjamin AT; Hirschhorn MD, 2007, 'A combinatorial solution to intertwined recurrences', Australasian Journal of Combinatorics, 37, pp. 101 - 116
Journal articles | 2007
Cooper S; Hirschhorn MD, 2007, 'On the number of primitive representations of integers as sums of squares', Ramanujan Journal, 13, pp. 7 - 25, http://dx.doi.org/10.1007/s11139-006-0240-6
Journal articles | 2007
Hirschhorn MD; Sellers JA, 2007, 'On recent congruence results of Andrews and Paule for broken k-diamonds', Bulletin of the Australian Mathematical Society, 75, pp. 121 - 126
Hirschhorn MD, 2007, 'The alternating harmonic series', Mathematical Intelligencer, 29, pp. 4 - 5
Journal articles | 2006
Cooper S; Hirschhorn M, 2006, 'Sums of squares and sums of triangular numbers', Georgian Mathematical Journal, 13, pp. 675 - 686, http://dx.doi.org/10.1515/GMJ.2006.675
Journal articles | 2006
Hirschhorn MD; Sellers JA, 2006, 'Arithmetic properties of overpartitions into odd parts', Annals of Combinatorics, 10, pp. 353 - 367, http://dx.doi.org/10.1007/s00026-006-0293-7
Hirschhorn MD, 2006, 'The case of the mysterious sevens', International Journal of Number Theory, 2, pp. 213 - 216
Journal articles | 2005
Angell DD; Hirschhorn MD, 2005, 'A remarkable continued fraction', Bulletin of the Australian Mathematical Society, 72, pp. 45 - 52
Journal articles | 2005
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, 5, pp. A16
Journal articles | 2005
Doust IR; Hirschhorn MD; Ho J, 2005, 'Trigonometric identities, linear algebra, and computer algebra', American Mathematical Monthly, 112, pp. 155 - 164, http://dx.doi.org/10.2307/30037413
Journal articles | 2005
Hirschhorn MD; Sellers JA, 2005, 'An infinite family of overpartition congruences modulo 12', Integers: the Electronic Journal of Combinatorial Number Theory, 5, pp. A20 - A20
Journal articles | 2005
Hirschhorn MD; Sellers JA, 2005, 'Arithmetic relations for overpartitions', Journal of Combinatorial Mathematics and Combinatorial Computing, 53, pp. 65 - 73
Journal articles | 2005
Hirschhorn MD; Sellers JA, 2005, 'Further results for partitions into four squares of equal parity', ARS Combinatoria, 76, pp. 33 - 45
Cooper S; Hirschhorn MD, 2004, 'A combinatorial proof of a result from number theory', Integers: the Electronic Journal of Combinatorial Number Theory, 4
Barrucand P; Cooper S; Hirschhorn MD, 2002, 'Results of Hurwitz type for five or more squares', Ramanujan Journal, 6, pp. 347 - 367, http://dx.doi.org/10.1023/A:1019753500261
Journal articles | 2002
Barrucand P; Hirschhorn MD, 2002, 'Formulae asociated with 5, 7, 9 and 11 squares', Bulletin of the Australian Mathematical Society, 65, pp. 503 - 510
Journal articles | 2002
Brown PG; Hirschhorn MD, 2002, 'A note on the Pell equation x2-(m2-4)y2 =1', Australian Mathematical Society Gazette, 29, pp. 273 - 276
Journal articles | 2002
Hirschhorn MD, 2002, 'Binomial coefficient identities and hyjpergeometric series', Australian Mathematical Society Gazette, 29, pp. 203 - 208
Journal articles | 2002
Hirschhorn MD, 2002, 'K-Gon partitions', Bulletin of the Australian Mathematical Society, 66, pp. 149 - 150
Journal articles | 2002
Hirschhorn MD, 2002, 'On sums of squares', Australian Mathematical Society Gazette, 29, pp. 86 - 87
Journal articles | 2002
Hirschhorn MD, 2002, 'There are infinitely many prime numbers', Australian Mathematical Society Gazette, 29, pp. 103 - 103
Journal articles | 2001
Cooper S; Hirschhorn MD, 2001, 'On some infinite product identities', Rocky Mountain Journal of Mathematics, 31, pp. 131 - 139, http://dx.doi.org/10.1216/rmjm/1008959672
Journal articles | 2001
Cooper S; Hirschhorn MD, 2001, 'On some sum-to-product identities', Bulletin of the Australian Mathematical Society, 63, pp. 353 - 365
Journal articles | 2001
Hirschhorn MD, 2001, 'On partitions into four distinct squares of equal parity', Australasian Journal of Combinatorics, 24, pp. 285 - 291
Cooper S; Hirschhorn MD; Lewis RA, 2000, 'Powers of Euler`s product and related identities', Ramanujan Journal, 4, pp. 137 - 155, http://dx.doi.org/10.1023/A:1009827103485
Journal articles | 2000
Hirschhorn MD, 2000, 'A proof of Eperson`s conjecture', Mathematical Gazette, pp. 442 - 446
Journal articles | 2000
Hirschhorn MD, 2000, 'An identity of Ramanujan, and applications', Contemporary Mathematics, pp. 229 - 234
Hirschhorn MD, 2000, 'Partial fractions and four classical theorems of number theory', American Mathematical Monthly, 107, pp. 260 - 263, http://dx.doi.org/10.2307/2589321
Journal articles | 2000
Hirschhorn MD, 2000, 'Partiy results for certain partition functions', Ramanujan Journal, pp. 129 - 135
Hirschhorn MD, 2000, 'Triangles with integer sides, revisited', Mathematics Magazine, pp. 53 - 56
Journal articles | 2000
Hirschhorn MD, 2000, 'Winquist and the Atkin- Swinnerton-Dyer partition congruences for modulus 11', Australasian Journal of Combinatorics, 22, pp. 101 - 104
Journal articles | 1999
Hirschhorn A; Hirschhorn MD; Hirschhorn P, 1999, 'The pizza theorem', Australian Mathematical Society Gazette, pp. 120 - 121
Journal articles | 1999
Hirschhorn MD; Sellers JA, 1999, 'On representations of a number as a sum of three squares', Discrete Mathematics, 199, pp. 85 - 101
Hirschhorn MD, 1998, 'Proofs of some hyperelliptic function identities', Bulletin of the Australian Mathematical Society, 58, pp. 465 - 468
Journal articles | 1998
Hirschhorn MD, 1998, 'The fundamental theorem of algebra', College Mathematics Journal, pp. 276 - 277
Journal articles | 1998
Hirschhorn MD, 1998, 'The sum sqrt 1 + sqrt 2 + ¿ + sqrt n without integration', Australian Mathematical Society Gazette, pp. 143 - 145
Journal articles | 1998
Hirschhorn MD, 1998, 'Three classical results or representations of a number', Seminaire Lotharingien de Combinatoire, pp. 41
Journal articles | 1998
Hirschhorn MD, 1998, 'Two diophantine equations studied by Ramanujan', Mathematics Magazine, pp. 386 - 388
Journal articles | 1998
Hirschhorn MD, 1998, 'Two or three identities of Ramanujan', American Mathematical Monthly, 105, pp. 52 - 54, http://dx.doi.org/10.2307/2589526
Journal articles | 1997
Hirschhorn MD, 1997, 'Radius of a buried pipe', Australian Mathematical Society Gazette, pp. 180 - 181
Journal articles | 1997
Hirschhorn MD, 1997, 'The volume of a cone, without calculus', Mathematics Magazine, pp. 295 - 296
Journal articles | 1996
Hirschhorn MD; Sellers JA, 1996, 'On representations of a number as a sum of three triangles', ACTA Arithmetica, 77, pp. 289 - 301, http://dx.doi.org/10.4064/aa-77-3-289-301
Hirschhorn MD, 1994, 'Several Identities in Statistical Mechanics', International Journal of Mathematics and Mathematical Sciences, 17, pp. 817 - 820, http://dx.doi.org/10.1155/S0161171294001146
Hirschhorn MD, 1988, 'A generalisation of the quintuple product identity', Journal of the Australian Mathematical Society, 44, pp. 42 - 45, http://dx.doi.org/10.1017/S1446788700031359
Hirschhorn MD; Hunt DC, 1985, 'Equilateral convex pentagons which tile the plane', Journal of Combinatorial Theory, Series A, 39, pp. 1 - 18, http://dx.doi.org/10.1016/0097-3165(85)90078-0
Journal articles | 1984
Guttmann AJ; Hirschhorn M, 1984, 'Comment on the number of spiral self-avoiding walks', Journal of Physics A: General Physics, 17, pp. 3613 - 3614, http://dx.doi.org/10.1088/0305-4470/17/18/029
Journal articles | 1983
Hirschhorn MD, 1983, 'A Simple proof of an identity of Ramanujan', Journal of the Australian Mathematical Society, 34, pp. 31 - 35, http://dx.doi.org/10.1017/S1446788700019728
Journal articles | 1982
Hirschhorn MD, 1982, 'A Simple Proof of Jacobi’s Four-Square Theorem', Journal of the Australian Mathematical Society, 32, pp. 61 - 67, http://dx.doi.org/10.1017/S144678870002440X
Journal articles | 1981
Hirschhorn MD; Hunt DC, 1981, 'A simple proof of the Ramanujan conjecture for powers of 5', Journal fur die Reine und Angewandte Mathematik, 1981, pp. 1 - 17, http://dx.doi.org/10.1515/crll.1981.326.1
Journal articles | 1981
Hirschhorn MD, 1981, 'Infinitely many identities of kolberg type', Journal of the Australian Mathematical Society, 31, pp. 20 - 25, http://dx.doi.org/10.1017/S1446788700018450
Hirschhorn MD; Loxton JH, 1975, 'Congruence properties of the binary partition function', Mathematical Proceedings of the Cambridge Philosophical Society, 78, pp. 437 - 442, http://dx.doi.org/10.1017/S0305004100051896
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 | 1999
Hirschhorn MD; Mcgowan JA, 1999, '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 | 1999
Hirschhorn MD; Sellers JA, 1999, '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