Superization and $(q,t)$-Specialization in Combinatorial Hopf Algebras

Jean-Christophe Novelli, Jean-Yves Thibon


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 Björner-Wachs $q$-hook-length formulas for binary trees, and similar formulas for plane trees.

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