Combinatorial properties of the numbers of tableaux of bounded height

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We introduce an infinite family of lower triangular matrices $Γ^{(s)}$, where $γ_{n,i}^s$ counts the standard Young tableaux on $n$ cells and with at most $s$ columns on a suitable subset of shapes. We show that the entries of these matrices satisfy a three-term row recurrence and we deduce recursive and asymptotic properties for the total number $τ_s(n)$ of tableaux on $n$ cells and with at most $s$ columns.
11 pages, 1 figure

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Combinatorics, 05E10. 05A15

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http://salesiana.dossiersoluciones.com/handle/123456789/156899

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0803.2112
 http://arxiv.org/abs/0803.2112

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arXiv