Multigraded combinatorial Hopf algebras and refinements of odd and even subalgebras

Details Multigraded combinatorial Hopf algebras and refinements of odd and even subalgebras Multigraded combinatorial Hopf algebras and refinements of odd and even subalgebras

2009-10-30

arxiv.org/abs/0910.5773v2

J. Algebr. Comb. 34 (2011), pages 451-506

Mathematics

Combinatorics

49 pages. To appear in the Journal of Algebraic Combinatorics

Scientific paper

We develop a theory of multigraded (i.e., $N^l$-graded) combinatorial Hopf algebras modeled on the theory of graded combinatorial Hopf algebras developed by Aguiar, Bergeron, and Sottile [Compos. Math. 142 (2006), 1--30]. In particular we introduce the notion of canonical $k$-odd and $k$-even subalgebras associated with any multigraded combinatorial Hopf algebra, extending simultaneously the work of Aguiar et al. and Ehrenborg. Among our results are specific categorical results for higher level quasisymmetric functions, several basis change formulas, and a generalization of the descents-to-peaks map.

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