- Title
- The distributions of the entries of Young tableaux
- Author(s)
- Morse, Jennifer
- Keywords
- Young Tableau; Hook Formula; Probability Distribution; Quasirandom; Subtableau
- Date
- 2001-06-11
- 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.
- Citation
- Retrieved November 2, 2007 from http://xxx.lanl.gov/find/grp_math/1/au:+Morse_J/0/1/0/all/0/1.
- URI
- http://lanl.arxiv.org/abs/math/0008160v3; http://hdl.handle.net/1860/1943
- In Collections
- Drexel Research