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

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

2011-01-18

arxiv.org/abs/1101.3427v1

Mathematics

Combinatorics

23 pages, 3 figures

Scientific paper

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.

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