𝑆_{∞} representations and combinatorial identities

Regev, Amitai

doi:10.1090/S0002-9947-01-02772-6

$S_{\infty }$ 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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