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Hopf Algebras and Edge-Labeled Posets

✍ Scribed by Nantel Bergeron; Frank Sottile

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 440 KB
Volume: 216
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7794

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✦ Synopsis

Given a finite graded poset with labeled Hasse diagram, we construct a quasisymmetric generating function for chains whose labels have fixed descents. This is a common generalization of a generating function for the flag f-vector defined by Ehrenborg and of a symmetric function associated with certain edge-labeled posets that arose in the theory of Schubert polynomials. We show that this construction gives a Hopf morphism from an incidence Hopf algebra of edge-labeled posets to the Hopf algebra of quasi-symmetric functions.

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