Colored posets and colored quasisymmetric functions

Abstract

The colored quasisymmetric functions, like the classic quasisymmetric functions, are known to form a Hopf algebra with a natural peak subalgebra. We show how these algebras arise as the image of the algebra of colored posets. To effect this approach we introduce colored analogs of $P$-partitions and enriched $P$-partitions. We also frame our results in terms of Aguiar, Bergeron, and Sottile's theory of combinatorial Hopf algebras and its colored analog.

31 pages, 5 figures

References in corpus (2)

• Free quasi-symmetric functions of arbitrary level
• The Hopf algebras of type B quasisymmetric functions and peak functions