A new proof of the refined alternating sign matrix theorem

Details A new proof of the refined alternating sign matrix theorem A new proof of the refined alternating sign matrix theorem

2005-07-13

arxiv.org/abs/math/0507270v1

Mathematics

Combinatorics

Scientific paper

In the early 1980s, Mills, Robbins and Rumsey conjectured, and in 1996 Zeilberger proved a simple product formula for the number of $n \times n$ 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.

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