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.

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