Explicit monomial expansions of the generating series for connection coefficients

Details Explicit monomial expansions of the generating series for connection coefficients Explicit monomial expansions of the generating series for connection coefficients

2011-11-27

arxiv.org/abs/1111.6215v1

Mathematics

Combinatorics

Scientific paper

This paper is devoted to the explicit computation of generating series for the connection coefficients of two commutative subalgebras of the group algebra of the symmetric group, the class algebra and the double coset algebra. As shown by Hanlon, Stanley and Stembridge (1992), these series gives the spectral distribution of some random matrices that are of interest to statisticians. Morales and Vassilieva (2009, 2011) found explicit formulas for these generating series in terms of monomial symmetric functions by introducing a bijection between partitioned hypermaps on (locally) orientable surfaces and some decorated forests and trees. Thanks to purely algebraic means, we recover the formula for the class algebra and provide a new simpler formula for the double coset algebra. As a salient ingredient, we derive a new explicit expression for zonal polynomials indexed by partitions of type [a,b,1^(n-a-b)].

Affiliated with

Also associated with

No associations

Rating

Explicit monomial expansions of the generating series for connection coefficients does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Explicit monomial expansions of the generating series for connection coefficients, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Explicit monomial expansions of the generating series for connection coefficients will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-686728