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Please use this identifier to cite or link to this item: http://hdl.handle.net/1860/1943

Title: The distributions of the entries of Young tableaux
Authors: Morse, Jennifer
Keywords: Young Tableau;Hook Formula;Probability Distribution;Quasirandom;Subtableau
Issue Date: 11-Jun-2001
Citation: Retrieved November 2, 2007 from http://xxx.lanl.gov/find/grp_math/1/au:+Morse_J/0/1/0/all/0/1.
Abstract: Let T be a standard Young tableau of shape λ ⊢ 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 → ∞, equal to f_/k!, where f_ is the number of all tableaux of shape λ. 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.
URI: http://lanl.arxiv.org/abs/math/0008160v3
Appears in Collections:Faculty Research and Publications (Mathematics)

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