Multigraded Combinatorial Hopf Algebras and Refinements of Odd and Even Subalgebras
Combinatorial Hopf algebra, Multigraded Hopf algebra, Quasisymmetric function, Symmetric function, Noncommutative symmetric function, Eulerian poset
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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Hsiao, S.K. and Karaali, G., Multigraded combinatorial Hopf algebras and refinements of odd and even subalgebras, Journal of Algebraic Combinatorics, Volume 34 Number 3 (November 2011), pages 451–506. MR2836370. doi: 10.1007/s10801-011-0279-3