Dr Thomas   Britz
Senior Lecturer

Dr Thomas Britz

Education

Science
School of Mathematics & Statistics

I am part of the Combinatorics Research Group at the School of Mathematics and Statistics here at UNSW Sydney.
See below for more details, and see my CV for comprehensive details, as well as my publications linked to on the right on this page.

If you are interested in graph theory, combinatorics or discrete mathematics, then feel free to email me or drop by and have a chat with me about prospective research and/or thesis topics!

 

PROFESSIONAL AFFILIATIONS AND SERVICE POSITIONS


President of the Combinatorial Mathematics Society of Australasia (CMSA) (December 2021 –)
Editor of Parabola (November 2015 –)
Managing Editor for the Australasian Journal of Combinatorics (August 2011 – )
Area Editor for the Journal of Algebra, Combinatorics, Discrete Structures and its Applications (April 2014 –)
Referee for 51 journals and 2 conference proceedings (roughly 150 reports)
Reviewer for Mathematical Reviews and Zentralblatt MATH (roughly 200 reviews)
Grant proposal assessor for ARC DP, NISDRG, FRP, Vidi (28 reports)
PhD Opponent (1 PhD defense)

Academic Mentor, UNSW (2019 – )
First Responder, UNSW (July 2018 – )
Academic Advisor, MATH, UNSW (August 2010 – )

Member of UNSW Student Wellbeing Community of Practice, UNSW (January 2022 – )
Member of UNSW Data Science Hub (uDASH), UNSW (August 2021 –)
Member of the Sustainability Committee, MATH, UNSW (February 2020 –)
Member of the Education Excellence Committee, Science Faculty, UNSW (March 2018 – ) 
Co-organiser of the 42th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing, UNSW, December 2019 (March 2018 – December 2019)
School liaison for the UNSW MathSoc, MATH, UNSW (Jan 2012 – 2018)
Chair of the Publicity Committee, MATH, UNSW (July 2014 – September 2018)
Lecturer's Representative for the School Standing Committee, UNSW (June 2011 – 2018)
Manager of Web and Social Media, MATH, UNSW (November 2017 – August 2018)
Member of the Computing Committee, MATH, UNSW (February 2018 – August 2018)
Member of the Research Committee, MATH, UNSW (October 2015 – July 2017)
Pure Representative on the Postgraduate Committee, MATH, UNSW (September 2013 – September 2017)
Chair of the School Standing Committee, MATH, UNSW (February 2014 – April 2015)
Member of the Policy and Resources Committee, MATH, UNSW (February – December 2014)
Organiser of Pure Departmental Seminar, School of Mathematics \&\ Statistics, UNSW (Aug 2010 – Jan 2013)
Co-organiser of the Joint Colloquium, School of Mathematics and Statistics, UNSW (Aug 2010 – Jan 2013)
Co-organiser of the 36th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing, UNSW, December 2012 (March 2011 – December 2012)

Member of the Australian Mathematical Society (August 2018 – )
Life member of the Combinatorial Mathematics Society of Australasia (CMSA)

I also enjoy a range of outreach activities, to promote mathematical thinking, learning and enjoyment.

Phone
9385 7115
Location
Room RC-5111, The Red Centre School of Mathematics and Statistics UNSW Sydney Sydney NSW 2052
  • Book Chapters | 2001
    Britz T; Mainetti M; Pezzoli L, 2001, 'Some operations on the family of equivalence relations', in Crapo H; Senato D (ed.), Algebraic Combinatorics and Computer Science. A Tribute To Gian-Carlo Rota, edn. Original, Springer-Verlag Italia, Milan, pp. 445 - 460
  • Journal articles | 2022
    Abel RJR; Britz T; Bunjamin YA; Combe D, 2022, 'Group divisible designs with block size 4 and group sizes 2 and 5', Journal of Combinatorial Designs, vol. 30, pp. 367 - 383, http://dx.doi.org/10.1002/jcd.21830
    Journal articles | 2022
    Abel RJR; Britz T; Bunjamin YA; Combe D, 2022, 'Group divisible designs with block size 4 where the group sizes are congruent to 2 mod 3', Discrete Mathematics, vol. 345, http://dx.doi.org/10.1016/j.disc.2021.112740
    Journal articles | 2021
    Britz T; Carey A; Gesztesy F; Nichols R; Sukochev F; Zanin D, 2021, 'The product formula for regularized Fredholm determinants', Proceedings of the American Mathematical Society, Series B, vol. 8, pp. 42 - 51, http://dx.doi.org/10.1090/bproc/70
    Journal articles | 2020
    Britz T; Mammoliti A; Shiromoto K, 2020, 'Wei-type duality theorems for rank metric codes', Designs, Codes, and Cryptography, vol. 88, pp. 1503 - 1519, http://dx.doi.org/10.1007/s10623-019-00688-9
    Journal articles | 2020
    Britz T; Cavenagh NJ; Mammoliti A; Wanless IM, 2020, 'Mutually orthogonal binary frequency squares', Electronic Journal of Combinatorics, vol. 27, pp. 1 - 26, http://dx.doi.org/10.37236/9373
    Journal articles | 2020
    Britz T; Co-author I, 2020, 'How to write a Parabola article', Parabola, vol. 56, https://www.parabola.unsw.edu.au/2020-2029/volume-56-2020/issue-2/article/how-write-parabola-article
    Journal articles | 2020
    Britz T, 2020, 'Fibonacci numbers: Brief history and counting problems', Parabola, vol. 56, https://www.parabola.unsw.edu.au/2020-2029/volume-56-2020/issue-1/article/fibonacci-numbers-brief-history-and-counting-problems
    Journal articles | 2018
    Tran B; Straka P; Falster MO; Douglas KA; Britz T; Jorm LR, 2018, 'Overcoming the data drought: Exploring general practice in Australia by network analysis of big data', Medical Journal of Australia, vol. 209, pp. 68 - 73, http://dx.doi.org/10.5694/mja17.01236
    Journal articles | 2018
    Mammoliti A; Britz T, 2018, 'On mubayi's conjecture and conditionally intersecting sets', SIAM Journal on Discrete Mathematics, vol. 32, pp. 2361 - 2380, http://dx.doi.org/10.1137/18M1166250
    Journal articles | 2018
    Britz T, 2018, 'On the betweenness centrality of trees, forests and cycles', Sustainable Forestry, vol. 1, pp. 1 - 5, http://dx.doi.org/10.24294/sf.v1i2.968
    Journal articles | 2017
    Bright D; Greenhill C; Britz T; Ritter A; Morselli C, 2017, 'Criminal network vulnerabilities and adaptations', Global Crime, vol. 18, pp. 424 - 441, http://dx.doi.org/10.1080/17440572.2017.1377614
    Journal articles | 2016
    Britz T; Shiromoto K, 2016, 'On the Covering Dimension of a Linear Code', IEEE Transactions on Information Theory, vol. 62, pp. 2694 - 2701, http://dx.doi.org/10.1109/TIT.2016.2538768
    Journal articles | 2016
    Hunter DO; Britz T; Jones M; Letnic M, 2016, 'Reintroduction of Tasmanian devils to mainland Australia can restore top-down control in ecosystems where dingoes have been extirpated: A response to Baker et al. 2016 and Fancourt & Mooney 2016', Biological Conservation, vol. 196, pp. 20 - 21, http://dx.doi.org/10.1016/j.biocon.2016.01.021
    Journal articles | 2015
    Hunter DO; Britz T; Jones M; Letnic MI, 2015, 'Reintroduction of Tasmanian devils to mainland Australia can restore top-down control in ecosystems where dingoes have been extirpated', Biological Conservation, vol. 191, pp. 428 - 435, http://dx.doi.org/10.1016/j.biocon.2015.07.030
    Journal articles | 2015
    Britz T; Shiromoto K; Westerbäck T, 2015, 'Demi-matroids from codes over finite Frobenius rings', Designs, Codes, and Cryptography, vol. 75, pp. 97 - 107, http://dx.doi.org/10.1007/s10623-013-9895-3
    Journal articles | 2015
    Britz T; Cavenagh NJ; Sørensen HK, 2015, 'Maximal partial Latin cubes', Electronic Journal of Combinatorics, vol. 22, http://dx.doi.org/10.37236/4726
    Journal articles | 2014
    Britz T; Johnsen T; Martin J, 2014, 'Chains, demi-matroids, and profiles', IEEE Transactions on Information Theory, vol. 60, pp. 986 - 991, http://dx.doi.org/10.1109/TIT.2013.2292524
    Journal articles | 2014
    Britz T; Mammoliti A; Sørensen HK, 2014, 'Proof by picture: A selection of nice picture proofs', Parabola, vol. 3, pp. 5 - 15, https://www.parabola.unsw.edu.au/2010-2019/volume-50-2014/issue-3/article/proof-picture-selection-nice-picture-proofs
    Journal articles | 2013
    Chan TH; Grant A; Britz T, 2013, 'Quasi-uniform codes and their applications', IEEE Transactions on Information Theory, vol. 59, pp. 7915 - 7926, http://dx.doi.org/10.1109/TIT.2013.2280914
    Journal articles | 2012
    Britz T; Johnsen T; Mayhew D; Shiromoto K, 2012, 'Wei-type duality theorems for matroids', Designs Codes and Cryptography, vol. 62, pp. 331 - 341, http://dx.doi.org/10.1007/s10623-011-9524-y
    Journal articles | 2010
    Britz T, 2010, 'Code enumerators and Tutte polynomials', IEEE Transactions on Information Theory, vol. 56, pp. 4350 - 4358, http://dx.doi.org/10.1109/TIT.2010.2054654
    Journal articles | 2009
    Britz T; Royle G; Shiromoto K, 2009, 'Designs from matroids', SIAM Journal on Discrete Mathematics, vol. 23, pp. 1082 - 1099, http://dx.doi.org/10.1137/080728913
    Journal articles | 2008
    Britz T; Shiromoto K, 2008, 'A MacWilliams type identity for matroids', Discrete Mathematics, vol. 308, pp. 4551 - 4559, http://dx.doi.org/10.1016/j.disc.2007.08.064
    Journal articles | 2008
    Britz T; Shiromoto K, 2008, 'Designs from subcode supports of linear codes', Designs Codes and Cryptography, vol. 46, pp. 175 - 189, http://dx.doi.org/10.1007/s10623-007-9145-7
    Journal articles | 2007
    Britz T, 2007, 'Higher support matroids', Discrete Mathematics, vol. 307, pp. 2300 - 2308, http://dx.doi.org/10.1016/j.disc.2006.12.001
    Journal articles | 2007
    Britz T, 2007, 'The Moore-Penrose inverse of a free matrix', Electronic Journal of Linear Algebra, vol. 16, pp. 208 - 215
    Journal articles | 2007
    Britz D; Britz T; Shiromoto K, 2007, 'The higher weight enumerators of the doubly-even self-dual [48,24,12] code', IEEE Transactions on Information Theory, vol. 53, pp. 2567 - 2571, http://dx.doi.org/10.1109/TIT.2007.899509
    Journal articles | 2006
    Britz T, 2006, 'On P-weight and P-distance inequalities', Discrete Mathematics, vol. 306, pp. 598 - 599, http://dx.doi.org/10.1016/j.disc.2006.01.017
    Journal articles | 2005
    Britz T, 2005, 'Extensions of the Critical Theorem', Discrete Mathematics, vol. 305, pp. 55 - 73, http://dx.doi.org/10.1016/j.disc.2005.10.002
    Journal articles | 2005
    Britz T; Olesky DD; van den Driessche P, 2005, 'Schur complements of matrices with acyclic bipartite graphs', Electronic Journal of Linear Algebra, vol. 14, pp. 2 - 11
    Journal articles | 2005
    Britz T; Rutherford CG, 2005, 'Covering radii are not matroid invariants', Discrete Mathematics, vol. 296, pp. 117 - 120, http://dx.doi.org/10.1016/j.disc.2005.03.002
    Journal articles | 2004
    Britz T; Mcdonald JJ; Olesky DD; van den Driessche P, 2004, 'Minimal spectrally arbitrary sign patterns', SIAM Journal on Matrix Analysis and Applications, vol. 26, pp. 257 - 271, http://dx.doi.org/10.1137/S0895479803432514
    Journal articles | 2004
    Britz T; Olesky DD; van den Driessche P, 2004, 'The Moore-Penrose inverse of matrices with an acyclic bipartite graph', Linear Algebra and its Applications, vol. 390, pp. 47 - 60, http://dx.doi.org/10.1016/j.laa.2004.04.007
    Journal articles | 2004
    Britz T; Olesky DD; van den Driessche P, 2004, 'Matrix inversion and digraphs: the one factor case', Electronic Journal of Linear Algebra, vol. 11, pp. 115 - 131
    Journal articles | 2003
    Britz T; Britz D, 2003, 'Mathematical proof of the consistency of Feldberg’s simple BDF start in electrochemical digital simulation', Journal of Electroanalytical Chemistry, vol. 546, pp. 123 - 125, http://dx.doi.org/10.1016/S0022-0728(03)00149-9
    Journal articles | 2002
    Britz T, 2002, 'MacWilliams identities and matroid polynomials', Electronic Journal of Combinatorics, vol. R9, pp. 1 - 19, http://www.combinatorics.org/Volume_9/Abstracts/v9i1r19.html
    Journal articles | 2001
    Britz T; Fomin S, 2001, 'Finite posets and Ferrers shapes', Advances in Mathematics, vol. 158, pp. 86 - 127, http://dx.doi.org/10.1006/aima.2000.1966
    Journal articles | 2001
    Britz T, 2001, 'The inverse of a non-singular free matrix', Linear Algebra and its Applications, vol. 338, pp. 245 - 249, http://dx.doi.org/10.1016/S0024-3795(01)00409-8
  • Preprints | 2021
    Abel RJR; Britz T; Bunjamin YA; Combe D, 2021, Group divisible designs with block size 4 and group sizes 2 and 5
    Preprints | 2021
    Li Z; Britz T, 2021, On the scale-freeness of random colored substitution networks, http://arxiv.org/abs/2109.14463v1
    Preprints | 2020
    Britz T; Carey A; Gesztesy F; Nichols R; Sukochev F; Zanin D, 2020, The product formula for regularized Fredholm determinants
    Software / Code | 2019
    Britz T; Bright D; Snoyman R, 2019, Criminal Networks, Published: 2019, Software / Code, https://rsnoyman.shinyapps.io/criminal_networks/
    Preprints | 2019
    Britz T; Cavenagh NJ; Mammoliti A; Wanless IM, 2019, Mutually orthogonal binary frequency squares
    Recorded / Rendered Creative Works | 2019
    Britz T, 2019, The Emotions of Mathematics, TEDx Talks, YouTube, Editor(s): TEDxUNSW , Published: 12 April 2019, Duration: 00:14:31, Recorded / Rendered Creative Works, https://youtu.be/Pp63Ot_l6Yk
    Other | 2018
    Henry B; Britz T; Schumacher E; Marschalek R; Zacarelli Denke R; Bojanic Helbingen C; Zayas Claure CD; Humenberger H; Fallas-Monge JJ; Durán Silva R; Jupri A; Kageyama K; Ishibashi I; Ávila Pozos O; Rivera I; Voss P; Panduro Urrelo HE; Karas S; Ruminska M; Sulitsa | O; Romanchuck V; Tolmachev Y, 2018, MATHBRIDGES Calendar, University of Münster, https://www.uni-muenster.de/imperia/md/content/afo/news/afo-kalender_mathebruecken_web.pdf
    Preprints | 2017
    Mammoliti A; Britz T, 2017, On Mubayi's Conjecture and conditionally intersecting sets
    Preprints | 2015
    Britz T; Shiromoto K, 2015, On the covering dimension of a linear code
    Conference Papers | 2010
    Chan TH; Grant A; Britz T, 2010, 'Properties of quasi-uniform codes', in 2010 IEEE International Symposium on Information Theory Proceedings, Austin, Texas, pp. 1153 - 1157, presented at 2010 IEEE International Symposium on Information Theory, Austin, Texas, 13 June 2010 - 18 June 2010, http://dx.doi.org/10.1109/ISIT.2010.5513674
    Software / Code | 2007
    Britz T; Britz D; Sørensen HK, 2007, Fast Tutte polynomial calculator, Maple, C++, Fortran, Published: 22 August 2007, Software / Code, http://www.thomasbritz.dk/notes/TuttePol-02a01.zip
    Theses / Dissertations | 2003
    Britz T, 2003, Matroids, Codes and Relations, University of Aarhus

Research Grants

$510,115 total awarded by grants, including the following:

  • ARC Discovery Grant: T. Britz,
    "Chromatic polynomials, random graphs, and error-correcting codes: a unified approach to graph colouring problems”, $242,066, 2007–2009
  • PIMS Postdoctoral Fellowship, 20,000CAD, 2003–2004
  • Villum Kann Rasmussen Postdoctoral Fellowship, 350.000DKK (2004–2005)
  • Carlsberg Foundation Postdoctoral Fellowship, 350.000DKK, 2006
  • UNSW Faculty of Science Silverstar Award, T. Britz, $25,000, 2013

Vice-Chancellor’s Award for Outstanding Contributions to Student Wellbeing, UNSW, 2021.
Science Dean's Award for Excellence in Student Wellbeing, UNSW, 2021.
Vice-Chancellor's Award for Contributions to Student Learning, UNSW, 2015.
UNSW Light Digital Uplift of MATH3411: $15,000, 2019.

I am interested in most areas of discrete mathematics and combinatorics. Most of my research has been so far in graph theory, matroid theory, coding theory, combinatorial polynomials, combinatorial matrix theory, partially ordered sets, matching theory, flow theory, and enumerative combinatorics. Most of my research is highly foundational and theoretical but I also enjoy applying combinatorial methods and results to other areas, so far including big data in medicine, bioinformatics, criminology, ecology, electrochemistry, law, linear algebra, and psycholinguistics. I also very much welcome the opportunity to solve tangible real-life problems and have consulted for a variety of companies.
If you have any problem that might benefit from some math- or problem-solving skills, then please email me!

I have designed, created and lectured the HDR/Honours courses

Aspects of Combinatorial Optimisation (at Kumamoto University, 2011)
Combinatorial Enumeration and Optimisation (AMSI Summer School 2012, with Prof. Ian Wanless).
MATH5505 - Combinatorics (UNSW 2016, 2018)
An Introduction to Combinatorics (Aalto University, 2017)

and written course material for, and lectured, the courses

MATH151 - Finite Mathematics (University of Victoria, BC, Canada)
MATH1081 - Discrete Mathematics
MATH1131 - Mathematics 1A
MATH1241 - Higher Mathematics 1B
MATH3411 - Information, Codes and Ciphers
MATH3521 - Algebraic Techniques in Number Theory

In total, I have lectured semester courses for 7,000 students.
I have also tutored numerous courses, for 2,000 students.

Here is quick access to some of my maths teaching and outreach videos.