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.