Doubly-refined enumeration of Alternating Sign Matrices and determinants of 2-staircase Schur functions
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چکیده
We prove a determinantal identity concerning Schur functions for 2staircase diagrams λ = (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.
منابع مشابه
A formula for the doubly refined enumeration of alternating sign matrices
Zeilberger [12] proved the Refined Alternating Sign Matrix Theorem, which gives a product formula, first conjectured by Mills, Robbins and Rumsey [9], for the number of alternating sign matrices with given top row. Stroganov [10] proved an explicit formula for the number of alternating sign matrices with given top and bottom rows. Fischer and Romik [7] considered a different kind of “doubly-ref...
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Zeilberger [12] proved the Refined Alternating Sign Matrix Theorem, which gives a product formula, first conjectured by Mills, Robbins and Rumsey [9], for the number of alternating sign matrices with given top row. Stroganov [10] proved an explicit formula for the number of alternating sign matrices with given top and bottom rows. Fischer and Romik [7] considered a different kind of “doubly-ref...
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The refined enumeration of alternating sign matrices (ASMs) of given order having prescribed behavior near one or more of their boundary edges has been the subject of extensive study, starting with the Refined Alternating Sign Matrix Conjecture of Mills-Robbins-Rumsey [25], its proof by Zeilberger [31], and more recent work on doublyrefined and triply-refined enumeration by several authors. In ...
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تاریخ انتشار 2011