Room 326

Alternating Sign Triangles: A new class of objects equinumerous with ASMs

Arvind Ayyer

IISc

We introduce a new class of square-ice configurations (also known as six-vertex model configurations) on triangular subsets of the square lattice, which we call Alternating Sign Triangles (ASTs). Surprisingly,
these turn out to be equinumerous with Alternating Sign Matrices (ASMs), with no simple bijection relating the two. The proof of the enumeration of ASTs follows from a generalisation of Kuperberg's proof for the enumeration of ASMs. We will explain the origin of this problem and the ideas involved in the proof. Time permitting, we will also give product formulas for other classes of square-ice configurations using similar ideas. This is joint work with Ilse Fischer and Roger Behrend.