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arxiv: 1101.3427 · v1 · pith:BJMVDPUEnew · submitted 2011-01-18 · 🧮 math.CO

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

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keywords alternatingfunctionsmatricessignconcerningdoubly-refinedenumerationsidentity
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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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