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, Duchon and Stroganov. This talk is based on joint work with Ilse Fischer and some ongoing work.

classical analysis and ODEscombinatoricsnumber theory

Audience: researchers in the topic

Special Functions and Number Theory seminar

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