Hopf Algebras and Edge-Labeled Posets

Details Hopf Algebras and Edge-Labeled Posets Hopf Algebras and Edge-Labeled Posets

1997-12-17

arxiv.org/abs/math/9712256v2

Journal of Algebra, 216 (1999), pp. 641-651

Mathematics

Combinatorics

LaTeX-2e, 9 pages. J. Algebra, to appear. Added examples, corrected typos, revised contents

Scientific paper

Given a finite graded poset with labeled Hasse diagram, we construct a quasi- symmetric generating function for (saturated) 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 to certain edge-labeled posets which arose in the theory of Schubert polynomials. We show this construction gives a Hopf morphism from an incidence algebra of edge-labeled posets to the Hopf algebra of quasi-symmetric functions.

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