Geodesic
Random Young Tableaux and Combinatorial Identities
Séminaire lotharingien de combinatoire, Tome 46 (2001-2002)
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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},
     year = {2001-2002},
     volume = {46},
     url = {http://geodesic.mathdoc.fr/item/SLC_2001-2002_46_a4/}
}
TY  - JOUR
AU  - Grigori Olshanski
AU  - Amitai Regev
TI  - Random Young Tableaux and Combinatorial Identities
JO  - Séminaire lotharingien de combinatoire
PY  - 2001-2002
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UR  - http://geodesic.mathdoc.fr/item/SLC_2001-2002_46_a4/
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%A Amitai Regev
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%J Séminaire lotharingien de combinatoire
%D 2001-2002
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%F SLC_2001-2002_46_a4
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/