Transactions of the American Mathematical Society

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$S_{\infty }$ representations and combinatorial identities
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by Amitai Regev
Trans. Amer. Math. Soc. 353 (2001), 4371-4404
DOI: https://doi.org/10.1090/S0002-9947-01-02772-6
Published electronically: 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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Bibliographic 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