Department of Mathematical Sciences
Stefano Lia, Umea University
Thursday, February 26th, 2026
12:00PM-12:50PM
Olin Hall 218
Speaker: Stefano Lia, Umea University
Title: On a Generalisation of Latin Squares Based on Alternating Sign Matrices
Abstract: Latin squares are fascinating classical objects in combinatorics with a well-developed structural theory. In a 2018 paper, Brualdi and Dahl introduced a generalisation of Latin squares obtained by replacing permutation matrices with alternating sign matrices (ASMs), while preserving natural row and column conditions.
In this talk, we review basic properties of Latin squares and describe this ASM-based generalisation. We then discuss recent results, obtained in joint work with A. Ernst, C. O'Brien, J. Zumbrägel, and J. Sheekey, that address some open questions posed by Brualdi and Dahl and clarify how certain structural properties of Latin squares extend to the ASM setting.