The # product in combinatorial Hopf algebras

We show that the # product of binary trees introduced by Aval and Viennot [arXiv:0912.0798] is in fact defined at the level of the free associative algebra, and can be extended to most of the classical combinatorial Hopf algebras.Comment: 20 page

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

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.Comment: 30 page

Noncommutative Symmetric Functions and an Amazing Matrix

We present a simple way to derive the results of Diaconis and Fulman [arXiv:1102.5159] in terms of noncommutative symmetric functions.Comment: 6 page