Refined enumeration of symmetry classes of Alternating Sign Matrices

Abstract: The sequence $1,1,2,7,42,429, \ldots$ counts several combinatorial objects, some of which I will describe in this talk. The major focus would be one of these objects, alternating sign matrices (ASMs). ASMs are square matrices with entries in the set $\{0,1,-1\}$, where non-zero entries alternate in sign along rows and columns, with all row and column sums being 1. I will discuss some questions that are central to the theme of ASMs, mainly dealing with their enumeration. In particular we shall prove some conjectures of Fischer, Robbins and Duchon. This is based on joint work with Ilse Fischer.

commutative algebraalgebraic topologycombinatorics

Audience: researchers in the topic

Applications of Combinatorics in Algebra, Topology and Graph Theory

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