Séminaire Lotharingien de Combinatoire, B46e (2001), 30 pp.
Grigori Olshanski and Amitai Regev
Random Young Tableaux and Combinatorial Identities
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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