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Dr Thomas Britz

Dr Thomas Britz

Senior Lecturer

Education

Science
School of Mathematics & Statistics

I am part of the at the here at UNSW Sydney.

PROFESSIONAL AFFILIATIONS AND SERVICE POSITIONS

President of the (CMSA) (December 2021 –)
Friend of the Australian Council of Heads of Mathematical Sciences (December 2021 – )
Chief Editor of (November 2015 –)
Managing Editor for the (August 2011 – )
Area Editor for the (April 2014 –October 2023)
Referee for 61 journals and 2 conference proceedings (> 175 reports)
Reviewer for Mathematical Reviews and Zentralblatt MATH (> 250 reviews)
Grant proposal assessor for ARC DP, NISDRG, FRP, Vidi (32 reports)
PhD Opponent/Assessor (2 times)

Member of the Hybrid Learning and Teaching Community of Practice, UNSW (May 2023 – )
Member of UNSW Student Wellbeing Community of Practice, UNSW (January 2022 –)
Academic Mentor, UNSW (2019– )
First Responder, UNSW (July 2018– )
Academic Advisor, MATH, UNSW (August 2010– )

Member of the Education Excellence Committee, Science Faculty, UNSW (March 2018 –)
Member of (uDASH), UNSW (August 2021 – 2024)
Member of the Sustainability Committee, MATH, UNSW (February 2020 – 2023)
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 (August 2018 – )
Life member of the (CMSA)

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

Phone
9385 7115
Location
Room RC-5111, School of Mathematics and Statistics Anita B. Lawrence Centre UNSW Sydney Sydney NSW 2052
  • Books | 2024
    Angell D; Britz T, 2024, Parabolic Problems 60 Years of Mathematical Puzzles in Parabola, CRC Press
  • Book Chapters | 2022
    Britz T; Cameron PJ, 2022, 'Codes', in Ellis-Monaghan JA; Moffatt I (ed.), Handbook of the Tutte Polynomial, Chapman & Hall/CRC, pp. 328 - 344,
    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, Springer-Verlag Italia, Milan, pp. 445 - 460
  • Journal articles | 2025
    Wang C; Abel RJR; Britz T; Bunjamin YA; Combe D, 2025, 'Group divisible designs with block size 4 and group sizes 4 and 10 and some other 4-GDDs', Discrete Mathematics, 348, pp. 114254,
    Journal articles | 2024
    Abel RJR; Britz T; Bunjamin YA; Combe D, 2024, 'Group divisible designs with block size 4 and group sizes 4 and 7', Journal of Combinatorial Designs, 32, pp. 328 - 346,
    Journal articles | 2024
    Abel RJR; Britz T; Bunjamin YA; Combe D, 2024, 'Group divisible designs with block size 4 and group sizes 4 and 7', Journal of Combinatorial Designs, 32, pp. 328 - 346,
    Journal articles | 2024
    Britz T; Chakraborty HS; Ishikawa R; Miezaki T; Tang HC, 2024, 'Harmonic Tutte polynomials of matroids II', Designs, Codes, and Cryptography, 92, pp. 1279 - 1297,
    Journal articles | 2024
    Britz T, 2024, 'Book review of Vector: A Surprising Story of Space, Time, and Mathematical Transformation', Parabola, 60,
    Journal articles | 2024
    Chng ZY; Britz T; Tan TS; Wong KB, 2024, 'The Ramsey Numbers for Trees of Large Maximum Degree Versus the Wheel Graph W8', Bulletin of the Malaysian Mathematical Sciences Society, 47, pp. 134,
    Journal articles | 2024
    Li NZ; Britz T, 2024, 'ON THE SCALE-FREENESS OF RANDOM COLORED SUBSTITUTION NETWORKS', Proceedings of the American Mathematical Society, 152, pp. 1377 - 1389,
    Journal articles | 2023
    Abel RJR; Britz T; Bunjamin YA; Combe D; Feng T, 2023, 'Group divisible designs with block size 4 where the group sizes are congruent to 1 mod 3', Discrete Mathematics, 346, pp. 113277,
    Journal articles | 2023
    Gilmore N; Britz T; Maartensson E; Orbegoso-Jordan C; Schroder S; Malerba M, 2023, 'Continental-scale assessment of micro-pumped hydro energy storage using agricultural reservoirs', Applied Energy, 349, pp. 121715,
    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, 30, pp. 367 - 383,
    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, 345, pp. 112740,
    Journal articles | 2022
    Britz T, 2022, 'The beauty of the Golden Ratio', Parabola, 58,
    Journal articles | 2020
    Britz T; Carey A; Gesztesy F; Nichols R; Sukochev F; Zanin D, 2020, 'The product formula for regularized Fredholm determinants', Proceedings of the American Mathematical Society, Series B, 8, pp. 42 - 51,
    Journal articles | 2020
    Britz T; Cavenagh NJ; Mammoliti A; Wanless IM, 2020, 'Mutually orthogonal binary frequency squares', Electronic Journal of Combinatorics, 27, pp. 1 - 26,
    Journal articles | 2020
    Britz T; Co-author I, 2020, 'How to write a Parabola article', Parabola, 56,
    Journal articles | 2020
    Britz T; Mammoliti A; Shiromoto K, 2020, 'Wei-type duality theorems for rank metric codes', Designs, Codes, and Cryptography, 88, pp. 1503 - 1519,
    Journal articles | 2020
    Britz T, 2020, 'Fibonacci numbers: Brief history and counting problems', Parabola, 56,
    Journal articles | 2018
    Britz T, 2018, 'On the betweenness centrality of trees, forests and cycles', Sustainable Forestry, 1, pp. 1 - 5,
    Journal articles | 2018
    Mammoliti A; Britz T, 2018, 'On mubayi's conjecture and conditionally intersecting sets', SIAM Journal on Discrete Mathematics, 32, pp. 2361 - 2380,
    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, 209, pp. 68 - 73,
    Journal articles | 2017
    Bright D; Greenhill C; Britz T; Ritter A; Morselli C, 2017, 'Criminal network vulnerabilities and adaptations', Global Crime, 18, pp. 424 - 441,
    Journal articles | 2017
    Britz T, 2017, 'Geoffrey Marnell: Mathematical Doodlings - Curiosities, Conjectures and Challenges', Parabola, 53,
    Journal articles | 2016
    Britz T; Shiromoto K, 2016, 'On the Covering Dimension of a Linear Code', IEEE Transactions on Information Theory, 62, pp. 2694 - 2701,
    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, 196, pp. 20 - 21,
    Journal articles | 2015
    Britz T; Cavenagh NJ; Sørensen HK, 2015, 'Maximal partial Latin cubes', Electronic Journal of Combinatorics, 22,
    Journal articles | 2015
    Britz T; Shiromoto K; Westerbäck T, 2015, 'Demi-matroids from codes over finite Frobenius rings', Designs, Codes, and Cryptography, 75, pp. 97 - 107,
    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,
    Journal articles | 2014
    Britz T; Johnsen T; Martin J, 2014, 'Chains, demi-matroids, and profiles', IEEE Transactions on Information Theory, 60, pp. 986 - 991,
    Journal articles | 2014
    Britz T; Mammoliti A; Sørensen HK, 2014, 'Proof by picture: A selection of nice picture proofs', Parabola, 3, pp. 5 - 15,
    Journal articles | 2013
    Chan TH; Grant A; Britz T, 2013, 'Quasi-uniform codes and their applications', IEEE Transactions on Information Theory, 59, pp. 7915 - 7926,
    Journal articles | 2012
    Britz T; Johnsen T; Mayhew D; Shiromoto K, 2012, 'Wei-type duality theorems for matroids', Designs Codes and Cryptography, 62, pp. 331 - 341,
    Journal articles | 2010
    Britz T, 2010, 'Code enumerators and Tutte polynomials', IEEE Transactions on Information Theory, 56, pp. 4350 - 4358,
    Journal articles | 2009
    Britz T; Royle G; Shiromoto K, 2009, 'Designs from matroids', SIAM Journal on Discrete Mathematics, 23, pp. 1082 - 1099
    Journal articles | 2008
    Britz T; Shiromoto K, 2008, 'A MacWilliams type identity for matroids', Discrete Mathematics, 308, pp. 4551 - 4559,
    Journal articles | 2008
    Britz T; Shiromoto K, 2008, 'Designs from subcode supports of linear codes', Designs Codes and Cryptography, 46, pp. 175 - 189
    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, 53, pp. 2567 - 2571
    Journal articles | 2007
    Britz T, 2007, 'Higher support matroids', Discrete Mathematics, 307, pp. 2300 - 2308
    Journal articles | 2007
    Britz T, 2007, 'The Moore-Penrose inverse of a free matrix', Electronic Journal of Linear Algebra, 16, pp. 208 - 215
    Journal articles | 2006
    Britz T, 2006, 'On P-weight and P-distance inequalities', Discrete Mathematics, 306, pp. 598 - 599
    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, 14, pp. 2 - 11
    Journal articles | 2005
    Britz T; Rutherford CG, 2005, 'Covering radii are not matroid invariants', Discrete Mathematics, 296, pp. 117 - 120
    Journal articles | 2005
    Britz T, 2005, 'Extensions of the Critical Theorem', Discrete Mathematics, 305, pp. 55 - 73
    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, 26, pp. 257 - 271
    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, 11, pp. 115 - 131
    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, 390, pp. 47 - 60,
    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, 546, pp. 123 - 125
    Journal articles | 2002
    Britz T, 2002, 'MacWilliams identities and matroid polynomials', Electronic Journal of Combinatorics, R9, pp. 1 - 19,
    Journal articles | 2001
    Britz T; Fomin S, 2001, 'Finite posets and Ferrers shapes', Advances in Mathematics, 158, pp. 86 - 127
    Journal articles | 2001
    Britz T, 2001, 'The inverse of a non-singular free matrix', Linear Algebra and its Applications, 338, pp. 245 - 249,
    Journal articles | 1988
    Britz T; Britz D, 1988, 'Transform (Type-In)', Amstrad Action, 32
  • Preprints | 2024
    Abel RJR; Britz T; Bunjamin YA; Combe D, 2024, Direct constructions of some group divisible designs with block size $4$ and up to $50$ points,
    Preprints | 2024
    Britz T; Chakraborty HS; Miezaki T, 2024, Harmonic Tutte polynomials of matroids III,
    Preprints | 2023
    Abel RJR; Britz T; Bunjamin YA; Combe D, 2023, Group divisible designs with block size 4 and group sizes 4 and 7, ,
    Preprints | 2022
    Britz T; Chakraborty HS; Ishikawa R; Miezaki T; Tang HC, 2022, Harmonic Tutte polynomials of matroids II, ,
    Preprints | 2022
    Britz T; Hu X; Islam A; Tang HC, 2022, Bounds on the closeness centrality of a graph, ,
    Recorded / Rendered Creative Works | 2022
    Britz T, 2022, How to create a supportive learning community, UNSW eLearning, Editor(s): Britz T, Published: 07 March 2022, Duration: 00:13:39, Recorded / Rendered Creative Works,
    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 NZ; Britz T, 2021, On the scale-freeness of random colored substitution networks, ,
    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,
    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,
    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,
    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, presented at 2010 IEEE International Symposium on Information Theory, Austin, Texas, 13 June 2010 - 18 June 2010
    Preprints | 2009
    Britz T; Heiseldel B; Johnsen T; Mayhew D; Shiromoto K, 2009, Generalizations of Wei's Duality Theorem, ,
    Software / Code | 2007
    Britz T; Britz D; Sørensen HK, 2007, Fast Tutte polynomial calculator, Maple, C++, Fortran, Published: 22 August 2007, Software / Code,
    Theses / Dissertations | 2003
    Britz T, 2003, Matroids, Codes and Relations, University of Aarhus
  • Media | 2023
    Britz T; Gilmore N; Malerba M, 2023, Farmers are famously self-reliant. Why not use farm dams as mini-hydro plants?, The Conversation Media Group Ltd,
    Media | 2023
    Britz T, 2023, The beauty of the Golden Ratio, Faculti Media Limited, ,
    Media | 2023
    Britz T, 2023, What is combinatorics?, Faculti Media Limited,
    Media | 2022
    Britz T, 2022, Does Amber Heard really have the world’s most beautiful face? An expert explains why the Golden Ratio test is bogus, The Conversation Media Group Ltd,
    Media | 2022
    Britz T, 2022, The history and mystery of Tangram, the children's puzzle game that harbours a mathematical paradox or two, The Conversation Media Group Ltd,

Research Grants

$525,115 total awarded by grants, including the following:

  • 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
  • , T. Britz,$25,000, 2013
  • UNSW Light Digital Uplift of MATH3411: $15,000, 2019.

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.

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, design 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, energy-storage, law, linear algebra, oceanography, psycholinguistics, quantum mechanics and renewable energy. I also very much welcome the opportunity to solve tangible real-life problems and have consulted for a variety of companies and government.
If you have any problem that might benefit from some math- or problem-solving skills, then please email me!

My Research Supervision

Supervision:

PhD students:
Hopein Christofen Tang, UNSW, 2023–
John Fitzgerald, UNSW (joint supervision with Lyria Bennet Moses, UNSW Law, and Ben Hachey, USyd), 2015–
Zhi Yee Chng, UNSW (joint supervision with Tan Ta Sheng and Wong Kok Bin, University of Malaya), 2024
Adam Mammoliti, UNSW, 2019
James Ross, UNSW (secondary supervisor; primary supervisor: Catherine Greenhill), 2023
Haya Saeed Aldosari, UNSW (secondary supervisor; primary supervisor: Catherine Greenhill), 2020
Vicki Likourezos, UNSW (secondary supervisor; primary supervisor: Slava Kalyuga, UNSW Arts), 2016-2017
Peter Ayre, UNSW (secondary supervisor; primary supervisor: Catherine Greenhill), 2019
Ali Hussian Alkhaldi, UNSW (secondary supervisor; primary supervisor: Norman Wildberger), 2014

Master by Research students:
Nero Ziyu Li, UNSW, 2021
Sin Keong Tong, UNSW, 2019
Zhi Yee Chng, UNSW, 2017
Maria Fischer, UNSW, 2015
Marie-Louise Hoejlund Rasmussen, Technical University of Denmark, 2005

Honours students:
Phillip Tzioumis UNSW, 2024-
Hayden McLean, UNSW, 2023
Zhan Wei, UNSW, 2023
Rickey Wu, UNSW, 2023
Edmond Gao, UNSW, 2021
Ryan Snoyman, UNSW, 2020
David Morris, UNSW, 2020
Michael Libman, UNSW, 2019
Nelson Chen, UNSW, 2019
Daniel Tanios, UNSW, 2019
Jessica Dai, UNSW, 2018
Tyson Churcher, UNSW, 2016
Duncan Crowley, UNSW, 2016
Adam Mammoliti, UNSW, 2014
Elizabeth Alford, UNSW, 2012

Master by Coursework students:
Demetra Siountris, UNSW, 2020
Xin Hu, UNSW, 2019
Salha Ahmed Alshaikey, UNSW, 2012
Dalal Alanazi, UNSW, 2012
Saad Althobaiti, UNSW, 2012
Doug Han Yang, UNSW, 2009
Ali Alkhaldi, UNSW, 2009

Research Course Project:
Jovana Kolar, UNSW, 2021
Abdellah Islam, UNSW, 2020
Iker Carrera, UNSW, 2020
James Ross, UNSW, 2014

AMSI Summer Research Project:
Ariana Liu, UNSW, 2023
Jovana Kolar, UNSW, 2022
Tiana Tsung Ung, UNSW, 2021

Summer Research Project:
Tiana Tsung Ung, UNSW, 2020
Abdellah Islam, UNSW, 2020
Charlie Stinson, UNSW, 2019
Zijian Gao, UNSW, 2019
Rui Tong, UNSW, 2018
Jacky Huang, UNSW, 2018
Gary Liang, UNSW, 2015
Adam Mammoliti, UNSW, 2014
Steve Sui, UNSW, 2013
Kirsten Vo-Phuoc, UNSW, 2012
Sen Lin, UNSW, 2011

My Teaching

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)

andwritten 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 8,000 students.
I have also tutored numerous courses, for 2,000 students.

Here is quick access to some of my .