Combinatorial properties of the numbers of tableaux of bounded height

Details Combinatorial properties of the numbers of tableaux of bounded height Combinatorial properties of the numbers of tableaux of bounded height

2008-03-14

arxiv.org/abs/0803.2112v1

Mathematics

Combinatorics

11 pages, 1 figure

Scientific paper

We introduce an infinite family of lower triangular matrices $\Gamma^{(s)}$, where $\gamma_{n,i}^s$ 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 $\tau_s(n)$ of tableaux on $n$ cells and with at most $s$ columns.

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