|
iDEA: Drexel E-repository and Archives >
Drexel Academic Community >
College of Arts and Sciences >
Department of Mathematics >
Faculty Research and Publications (Mathematics) >
The distributions of the entries of Young tableaux
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
http://hdl.handle.net/1860/1943 |
| Appears in Collections: | Faculty Research and Publications (Mathematics)
|
Items in iDEA are protected by copyright, with all rights reserved, unless otherwise indicated.
|
www.drexel.edu
