Superization and $(q,t)$-Specialization in Combinatorial Hopf Algebras
Copyright policy )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 Björner-Wachs $q$-hook-length formulas for binary trees, and similar formulas for plane trees.
- French National Centre for Scientific Research France
- École des Ponts ParisTech France
- Paris-Est Sup France
- UNIVERSITE GUSTAVE EIFFEL France
Symmetric functions and generalizations, Connections of Hopf algebras with combinatorics, Mathematics - Rings and Algebras, 05E05, 16W30, superization process, Trees, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Rings and Algebras (math.RA), [MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA], FOS: Mathematics, Operads, Mathematics - Combinatorics, symmetric functions, Combinatorics (math.CO)
Symmetric functions and generalizations, Connections of Hopf algebras with combinatorics, Mathematics - Rings and Algebras, 05E05, 16W30, superization process, Trees, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Rings and Algebras (math.RA), [MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA], FOS: Mathematics, Operads, Mathematics - Combinatorics, symmetric functions, Combinatorics (math.CO)
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