Abstract
We develop a theory of multigraded (i.e., ℕl-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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This work began while S.K. Hsiao was supported by an NSF Postdoctoral Research Fellowship.
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Hsiao, S.K., Karaali, G. Multigraded combinatorial Hopf algebras and refinements of odd and even subalgebras. J Algebr Comb 34, 451–506 (2011). https://doi.org/10.1007/s10801-011-0279-3
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DOI: https://doi.org/10.1007/s10801-011-0279-3