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Descent Functions and Random Young Tableaux

Published online by Cambridge University Press:  25 June 2001

RON M. ADIN  and
YUVAL ROICHMAN
RON M. ADIN
Affiliation:
Department of Mathematics and Computer Science, Bar-Ilan University, Ramat-Gan 52900, Israel (e-mail: radin@math.biu.ac.il, yuvalr@math.biu.ac.il)
YUVAL ROICHMAN
Affiliation:
Department of Mathematics and Computer Science, Bar-Ilan University, Ramat-Gan 52900, Israel (e-mail: radin@math.biu.ac.il, yuvalr@math.biu.ac.il)
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Abstract

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The expectation of the descent number of a random Young tableau of a fixed shape is given, and concentration around the mean is shown. This result is generalized to the major index and to other descent functions. The proof combines probabilistic arguments together with combinatorial character theory. Connections with Hecke algebras are mentioned.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 10 , Issue 3 , May 2001 , pp. 187 - 201
Copyright
2001 Cambridge University Press