New enumeration formulas for alternating sign matrices and square ice partition functions
@article{Ayyer2012NewEF, title={New enumeration formulas for alternating sign matrices and square ice partition functions}, author={Arvind Ayyer and Dan Romik}, journal={Advances in Mathematics}, year={2012}, volume={235}, pages={161-186} }
15 Citations
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Alternating sign matrices (ASMs), polytopes and partially-ordered sets are fascinating combinatorial
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This paper consists of a review of results for the exact enumeration of alternating sign matrices of fixed size with prescribed values of some or all of the following six statistics: the numbers of…
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Inversions and the Gog-Magog problem
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We consider the problem of finding a bijection between the sets of alternating sign matrices and of totally symmetric self complementary plane partitions, which can be reformulated using Gog and…
Quantum integrable combinatorics of Schur polynomials
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We examine and present new combinatorics for the Schur polynomials from the viewpoint of quantum integrability. We introduce and analyze an integrable six-vertex model which can be viewed as a…
References
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Monotone triangles are plane integer arrays of triangular shape with certain monotonicity conditions along rows and diagonals. Their significance is mainly due to the fact that they correspond to n×n…
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We introduce a family of planar regions, called Aztec diamonds, and study tilings of these regions by dominoes. Our main result is that the Aztec diamond of order n has exactly 2n(n+1)/2 domino…