1999/10/29 by Ron M. Adin, Adin, Ron M., Yuval Roichman +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #math.CO #math.PR
paper · pdf · doi:10.48550/arxiv.math/9910165
20 pages, final form; to appear in Combinatorics, Probability and Computing
arxiv created 2000/11/05 · arxiv updated 2009/11/30
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.