arXiv Analytics

Sign in

arXiv:0710.2454 [math.CO]AbstractReferencesReviewsResources

Two positivity conjectures for Kerov polynomials

Michel Lassalle

Published 2007-10-12, updated 2008-01-27Version 4

Kerov polynomials express the normalized characters of irreducible representations of the symmetric group, evaluated on a cycle, as polynomials in the free cumulants of the associated Young diagram. We present two positivity conjectures for their coefficients. The latter are stronger than the positivity conjecture of Kerov-Biane, recently proved by Feray.

Comments: 15 pages, LaTeX, final version, to appear in Adv. Appl. Math
Journal: Advances in Applied Mathematics, 41 (2008), 407-422
Categories: math.CO, math.RT
Related articles: Most relevant | Search more
arXiv:0802.0448 [math.CO] (Published 2008-02-04, updated 2009-07-28)
Jack polynomials and free cumulants
arXiv:math/0605654 [math.CO] (Published 2006-05-24)
Constructing all irreducible Specht modules in a block of the symmetric group
arXiv:math/0411647 [math.CO] (Published 2004-11-30, updated 2005-10-21)
Asymptotics of characters of symmetric groups, genus expansion and free probability

Links

Toolbox