Identities for the number of standard Young tableaux in some $(k,\ell)$ hooks

Details Identities for the number of standard Young tableaux in some $(k,\ell)$ hooks Identities for the number of standard Young tableaux in some $(k,\ell)$ hooks

2010-03-09

arxiv.org/abs/1003.1835v2

Mathematics

Combinatorics

Scientific paper

Closed formulas are known for $S(k,0;n)$, the number of standard Young
tableaux of size $n$ and with at most $k$ parts, where $1\le k\le 5$. Here we
study the analogue problem for $S(k,\ell;n)$, the number of standard Young
tableaux of size $n$ which are contained in the $(k,\ell)$ hook. We deduce some
formulas for the cases $k+\ell\le 4$.

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