204 research outputs found
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
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
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
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