Homepage of John Irving

Last updated September 3, 2024

Who Am I?

I am an Associate Professor at Saint Mary's University in Halifax, Nova Scotia, Canada. I am currently Chair of the Department of Mathematics and Computing Science. My primary research interest is algebraic combinatorics, particularly enumerative problems underlying questions in geometry and representation theory.

Contact Information

office	MN 123
phone	(902) 420-5792
email	name.surname at smu.ca

mail	Dept. of Mathematics & Computing Science Saint Mary's University Halifax, NS, Canada, B3H 3C3

Office Hours

Tuesday	1:00–3:00
Wednesday	10:00–2:00
Thursday	12:30–2:30

Send me an e-mail if you wish to set up an appointment to see me outside of office hours, or drop by the office and see if I'm available.

Teaching

I am currently (Fall 2024) teaching Math 1211 (Introductory Calculus II) and Math 4420 (Abstract Algebra I).

Research

My main research interest is enumerative combinatorics (ie. counting), particularly as it relates to problems in algebra and geometry. To date I have mostly focused on problems involving factorizations in the symmetric group; that is, counting the number of ways a given permutation can be decomposed as an ordered product of other permutations with various conditions imposed on these factors (such as cycle type, minimality, transitivity). Questions of this type are intimately linked with the representation theory of the symmetric group (equivalently, the study of its group algebra), and also the geometry of branched coverings.

Preprints of my papers can be downloaded below. My graduate work was completed under the supervision of David Jackson at the University of Waterloo (Ontario, Canada). Both my Master's and Ph.D. theses are available upon request.

An Enumerative Problem Concerning Products of Permutations, Master's Thesis, University of Waterloo, 1998
Combinatorial Constructions for Transitive Factorizations in the Symmetric Group, Ph.D. Thesis, University of Waterloo, 2004
On the number of factorizations of a full cycle, J. Combin. Theory Ser. A, 113 (2006), 1549–1554
Minimal transitive factorizations of permutations into cycles, Canad. J. Math., 61 (2009), 1092–1117
(with A. Rattan) Minimal factorizations of permutations into star transpositions, Discrete Math., 309 (2009), 1435–1442
(with A. Rattan) The number of lattice paths below a cyclically shifting boundary, J. Combin. Theory Ser. A, 116 (2009), 499–514
(with G. Berkolaiko) Inequivalent factorizations of permutations, J. Combin. Theory Ser. A, 140 (2016), 1–37
(with A. Rattan) Trees, parking functions, and factorizations of full cycles, Europ. J. Combinatorics, 93 (2021)
(with A. Rattan) k-Factorizations of the full cycle and generalized Mahonian statistics on k-forests, Adv. Appl. Math., 151 (2023)
(with T. Kosir and M. Mastnak) A proof of the Box Conjecture for commuting pairs of matricess (preprint)
A generalized Burge correspondence and k-measure of partitions (preprint)

Please contact me if you have any questions or would like further information.