The number of monotone triangles with prescribed bottom row

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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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Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/73791

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0501102
 http://arxiv.org/abs/math/0501102

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arXiv