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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

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$S_{\infty }$ representations and combinatorial identities
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Trans. Amer. Math. Soc. 353 (2001), 4371-4404 Request permission

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
  • Received by editor(s): March 14, 1999
  • Published electronically: June 14, 2001
  • Additional Notes: This work was partially supported by ISF grant 6629/1
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 4371-4404
  • MSC (2000): Primary 20C32
  • DOI: https://doi.org/10.1090/S0002-9947-01-02772-6
  • MathSciNet review: 1851175