The number of monotone triangles with prescribed bottom row

Details The number of monotone triangles with prescribed bottom row The number of monotone triangles with prescribed bottom row

2005-01-07

arxiv.org/abs/math/0501102v1

Mathematics

Combinatorics

Scientific paper

We show that the number of monotone triangles with prescribed bottom row
(k_1,...,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 $n \times n$ alternating sign matrices.

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