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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