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Colored posets and colored quasisymmetric functions

Samuel K. Hsiao·T. Kyle Petersen
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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.

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Samuel K. Hsiao, T. Kyle Petersen. 2006-10-31. Colored posets and colored quasisymmetric functions. https://arxiv.org/abs/math/0610984

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