The distributions of the entries of Young tableaux

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:97

Article

McKay, BD

关键词: Young tableau;    hook formula;    probability distribution;    quasirandom;    subtableau;   

DOI  :  10.1006/jcta.2001.3200

来源: Elsevier

【 摘 要 】

Let T be a standard Young tableau of shape lambda proves 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 --> infinity, equal to f(lambda)/k!, where f(lambda) is the number of all tableaux of shape lambda. 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, (C) 2001 Elsevier Science.

【 授权许可】

Free