Doubly-refined enumeration of Alternating Sign Matrices and determinants of 2-staircase Schur functions

TL;DR

This paper establishes a determinantal identity for Schur functions associated with 2-staircase diagrams, linking it to the enumeration of Alternating Sign Matrices and the 6-vertex model at a special point.

Contribution

It introduces a new determinantal identity for Schur functions of 2-staircase diagrams, connecting combinatorial enumeration with algebraic identities.

Findings

Derived a determinantal identity for 2-staircase Schur functions

Connected Schur functions to the enumeration of Alternating Sign Matrices

Provided a new identity for doubly-refined ASM enumeration

Abstract

We prove a determinantal identity concerning Schur functions for 2-staircase diagrams lambda=(ln+l',ln,l(n-1)+l',l(n-1),...,l+l',l,l',0). When l=1 and l'=0 these functions are related to the partition function of the 6-vertex model at the combinatorial point and hence to enumerations of Alternating Sign Matrices. A consequence of our result is an identity concerning the doubly-refined enumerations of Alternating Sign Matrices.