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Colored Posets and Colored Quasisymmetric Functions
Samuel K. Hsiao1 and T. Kyle Petersen2
1Mathematics Program, Bard College, P.O. Box 5000, Annandale-on-Hudson, NY 12504, USA
hsiao@bard.edu
2Department of Mathematical Sciences, DePaul University, Chicago, IL 60614, USA
tkpeters@math.depaul.edu
Annals of Combinatorics 14 (2) pp.251-289 Summer, 2010
AMS Subject Classification: 16W30; 05E99; 06A07; 06A11
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.
Keywords: combinatorial Hopf algebra, poset, quasisymmetric function, peak algebra, P-partition, colored poset, colored quasisymmetric function, colored peak algebra, colored P-partition

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