A new proof of the refined alternating sign matrix theorem

2005/07/13 by Ilse Fischer, Fischer, Ilse · 1 citation
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Random Matrices and Applications #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.48550/arxiv.math/0507270

arxiv created 2005/07/13 · arxiv updated 2009/12/01

Abstract

In the early 1980s, Mills, Robbins and Rumsey conjectured, and in 1996 Zeilberger proved a simple product formula for the number of n × n alternating sign matrices with a 1 at the top of the i-th column. We give an alternative proof of this formula using our operator formula for the number of monotone triangles with prescribed bottom row. In addition, we provide the enumeration of certain 0-1-(-1) matrices generalizing alternating sign matrices.

Cited by

• Frozen-corner enumeration of Alternating Sign Matrices

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• A formula for the doubly-refined enumeration of alternating sign matrices
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