Hopf Algebras and Edge-Labeled Posets

Abstract

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.

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

References in corpus (1)

• Schubert polynomials, the Bruhat order, and the geometry of flag manifolds

Cited by in corpus (3)

• Non-commutative Pieri operators on posets
• Skew quasisymmetric Schur functions and noncommutative Schur functions
• Algebraic lattices in QFT renormalization