The number of monotone triangles with prescribed bottom row

2005/01/07 by Ilse Fischer, Fischer, Ilse
Computer Science · Mathematics · #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #math.CO #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0501102

arxiv created 2005/01/07 · openalex publication_date 2005/01/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the number of monotone triangles with prescribed bottom row (k₁,...,k_n) is given by a simple product formula which remarkably involves (shift) operators. Monotone triangles with bottom row (1,2,...,n) are in bijection with n × n alternating sign matrices.

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