We introduce an infinite family of lower triangular matrices $Gamma^(s)$, where $gamma^(s)_{n,i}$ counts the standard Young tableaux on n cells, with at most s columns, whose second and third column lengths differ by i. 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 s(n) of tableaux on n cells and with at most s columns.
Combinatorial properties of the numbers of tableaux of bounded height
BARNABEI, MARILENA;BONETTI, FLAVIO;SILIMBANI, MATTEO
2007
Abstract
We introduce an infinite family of lower triangular matrices $Gamma^(s)$, where $gamma^(s)_{n,i}$ counts the standard Young tableaux on n cells, with at most s columns, whose second and third column lengths differ by i. 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 s(n) of tableaux on n cells and with at most s columns.File in questo prodotto:
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