Geodesic
Random Young Tableaux and Combinatorial Identities
Séminaire lotharingien de combinatoire, Tome 46 (2001-2002)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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. 

@article{SLC_2001-2002_46_a4,
     author = {Grigori Olshanski and Amitai Regev},
     title = {Random {Young} {Tableaux} and {Combinatorial} {Identities}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {46},
     year = {2001-2002},
     url = {http://geodesic.mathdoc.fr/item/SLC_2001-2002_46_a4/}
}
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Grigori Olshanski; Amitai Regev. Random Young Tableaux and Combinatorial Identities. Séminaire lotharingien de combinatoire, Tome 46 (2001-2002). http://geodesic.mathdoc.fr/item/SLC_2001-2002_46_a4/