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$S_{\infty }$ representations and combinatorial identities

Author(s): Amitai Regev
Journal: Trans. Amer. Math. Soc. 353 (2001), 4371-4404.
MSC (2000): Primary 20C32
Posted: June 14, 2001
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Abstract: For various probability measures on the space of the infinite standard Young tableaux we study the probability that in a random tableau, the $(i,j)^{th}$ entry equals a given number $n$. Beside the combinatorics of finite standard tableaux, the main tools here are from the Vershik-Kerov character theory of $S_{\infty}$. The analysis of these probabilities leads to many explicit combinatorial identities, some of which are related to hypergeometric series.

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Additional Information:

Amitai Regev
Affiliation: Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel - and - Department of Mathematics, Pennsylvania State University, State College, Pennsylvania 16802
Address at time of publication: Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel
Email: regev@wisdom.weizmann.ac.il

DOI: 10.1090/S0002-9947-01-02772-6
PII: S 0002-9947(01)02772-6
Received by editor(s): March 14, 1999
Posted: June 14, 2001
Additional Notes: This work was partially supported by ISF grant 6629/1
Copyright of article: Copyright 2001, American Mathematical Society

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