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Transactions of the American Mathematical Society

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$S_{\infty }$ representations and combinatorial identities

Author: Amitai Regev
Journal: Trans. Amer. Math. Soc. 353 (2001), 4371-4404
MSC (2000): Primary 20C32
Published electronically: June 14, 2001
MathSciNet review: 1851175
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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

Received by editor(s): March 14, 1999
Published electronically: June 14, 2001
Additional Notes: This work was partially supported by ISF grant 6629/1
Article copyright: © Copyright 2001 American Mathematical Society

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