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An operator formula for the number of halved monotone triangles with prescribed bottom row

2007/02/22 by Ilse Fischer, Fischer, Ilse
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.math/0702637

arxiv created 2007/02/22 · arxiv updated 2009/12/01

Abstract

Monotone triangles are certain triangular arrays of integers, which correspond to n × n alternating sign matrices when prescribing (1,2,...,n) as bottom row of the monotone triangle. In this article we define halved monotone triangles, a specialization of which correspond to vertically symmetric alternating sign matrices. We derive an operator formula for the number of halved monotone triangles with prescribed bottom row which is analogous to our operator formula for the number of ordinary monotone triangle.

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