Superization and (q,t)-specialization in combinatorial Hopf algebras

Jean-Christophe Novelli, Jean-Yves Thibon

Published 2008-03-12Version 1

We extend a classical construction on symmetric functions, the superization process, to several combinatorial Hopf algebras, and obtain analogs of the hook-content formula for the (q,t)-specializations of various bases. Exploiting the dendriform structures yields in particular (q,t)-analogs of the Bjorner-Wachs q-hook-length formulas for binary trees, and similar formulas for plane trees.