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The Distributions of the Entries of Young Tableaux

✍ Scribed by Brendan D. McKay; Jennifer Morse; Herbert S. Wilf

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
109 KB
Volume
97
Category
Article
ISSN
0097-3165

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✦ Synopsis

Let T be a standard Young tableau of shape l * k. We show that the probability that a randomly chosen Young tableau of n cells contains T as a subtableau is, in the limit n Q ., equal to f l /k!, where f l is the number of all tableaux of shape l. In other words, the probability that a large tableau contains T is equal to the number of tableaux whose shape is that of T, divided by k!. We give several applications, to the probabilities that a set of prescribed entries will appear in a set of prescribed cells of a tableau, and to the probabilities that subtableaux of given shapes will occur. Our argument rests on a notion of quasirandomness of families of permutations, and we give sufficient conditions for this to hold.

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