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Séminaire Lotharingien de Combinatoire, B46e (2001), 30 pp.

# Grigori Olshanski and Amitai Regev

#
Random Young Tableaux and Combinatorial Identities

**Abstract.**
We derive new combinatorial identities which may be viewed
as multivariate analogs of summation formulas for hypergeometric
series. As in the previous paper by one of us
[*Trans. Amer. Math. Soc.* **353** (2001), 4371-4404],
we start with probability
distributions on the space of the infinite
Young tableaux. Then we calculate the probability that the entry of
a random tableau at a given box equals *n*=1,2,... Summing these
probabilities over *n* and equating the result to 1 we get a
nontrivial identity. Our choice for the initial distributions is
motivated by the recent work on harmonic analysis on the infinite
symmetric group and related topics.

Received: June 1, 2001; Accepted: July 24, 2001.

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