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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