Prof Ian Wanless

Research Overview

Prof Wanless has published over 100 papers across a wide range of discrete mathematical disciplines including graph theory, design theory, combinatorics, enumeration and algebra. He is a recognised authority on matrix permanents and Latin squares, having been invited to write chapters in CRC handbooks on both topics. He loves everything to do with the combinatorics of permutations including Latin hypercubes, permutation arrays, permutation polynomials and orthomorphisms.

He has worked on a wide range of combinatorial designs including Steiner triple systems, Hadamard matrices, orthogonal arrays, frequency squares and Heffter arrays. In graph theory he was worked on matchings, coverings, factorisations, graph polynomials and random graphs. His favourite problem in graph theory is the challenge of maximising the number of matchings in regular bipartite graphs. In algebra he has worked on combinatorial properties of Cayley tables, loops and quasigroups, cyclotomic properties of finite fields, Cayley graphs. He has worked on enumerations of many kind, both computational and asymptotic. He also has an interest in number theoretic properties of combinatorial numbers. One of his favourite results is that, mod n, the number of reduced Latin squares of order n is an indicator function for primality of n.

Selected Publications

[1] Bryant, Darryn Edward ; Maenhaut, Barbara ; Wanless, Ian Murray. "New families of atomic latin squares and perfect 1-factorisations". In: Journal of Combinatorial Theory - Series A. 2006 ; Vol. 113, No. 4. pp. 608 - 624. https://doi.org/10.1016/j.jcta.2005.05.003

[2] Maenhaut, Barbara ; Wanless, Ian Murray ; Webb, Bridget S. "Subsquare-free latin squares of odd order". In: European Journal of Combinatorics. 2007 ; Vol. 28. pp. 322 - 336. https://doi.org/10.1016/j.ejc.2005.07.002

[3] Cavenagh, Nicholas ; Greenhill, Catherine Suzanne ; Wanless, Ian Murray. "The cycle structure of two rows in a random latin square". In: Random Structures & Algorithms. 2008 ; Vol. 33, No. 3. pp. 286 - 309. https://doi.org/10.1002/rsa.20216

[4] Stones, Douglas Stuart ; Wanless, Ian Murray. "Divisors of the number of Latin rectangles". In: Journal of Combinatorial Theory - Series A. 2010 ; Vol. 117. pp. 204 - 215. https://doi.org/10.1016/j.jcta.2009.03.019

[5] Wanless, Ian Murray. "Counting matchings and tree-like walks in regular graphs". In: Combinatorics, Probability and Computing. 2010 ; Vol. 19, No. 3. pp. 463 - 480. https://doi.org/10.1017/S0963548309990678