On the Doubly Refined Enumeration of Alternating Sign Matrices and Totally Symmetric Self-Complementary Plane Partitions

TL;DR

This paper proves a deep combinatorial enumeration equivalence between two complex mathematical objects, Alternating Sign Matrices and Totally Symmetric Self-Complementary Plane Partitions, using advanced integral formula techniques.

Contribution

It establishes the equality of their doubly refined enumerations through novel integral formula methods derived from quantum algebra solutions.

Findings

Proves the enumeration equality between two combinatorial objects.

Uses integral formulae from quantum Knizhnik--Zamolodchikov solutions.

Advances understanding of symmetry and enumeration in combinatorics.

Abstract

We prove the equality of doubly refined enumerations of Alternating Sign Matrices and of Totally Symmetric Self-Complementary Plane Partitions using integral formulae originating from certain solutions of the quantum Knizhnik--Zamolodchikov equation.