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Séminaire Lotharingien de Combinatoire, B63c (2010), 8 pp.

# Amitai Regev

# Identities for the Number of Standard Young
Tableaux in some (*k*,*l*)-Hooks

**Abstract.**
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<=*k*<=5. Here we study the analogous problem
for *S*(*k*,*l*;*n*),
the number of standard Young tableaux of size
*n* which are contained in the (*k*,*l*)-hook. We deduce some
formulas for the cases *k*+*l*<=4.

Received: March 19, 2010.
Accepted: April 11, 2010.

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