#####
Séminaire Lotharingien de Combinatoire, B65f (2012), 25 pp.

# Philippe Biane, Luigi Cantini and Andrea Sportiello

# Doubly-Refined Enumeration of Alternating Sign Matrices
and Determinants of 2-Staircase Schur Functions

**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 numbers of Alternating Sign Matrices.

Received: February 1, 2012.
Revised: May 9, 2012.
Accepted: May 9, 2012.
Final Version: June 25, 2012.

The following versions are available: