Multigraded Combinatorial Hopf Algebras and Refinements of Odd and Even Subalgebras

Document Type

Article

Department

Mathematics (Pomona)

Publication Date

2011

Keywords

Combinatorial Hopf algebra, Multigraded Hopf algebra, Quasisymmetric function, Symmetric function, Noncommutative symmetric function, Eulerian poset

Abstract

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 et al. (Compos. Math. 142:1–30,2006). 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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© 2011 Springer, Part of Springer Science+Business Media

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