Hopf Algebras and Edge-Labeled Posets
Combinatorics
2016-11-08 v2 Quantum Algebra
Rings and Algebras
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.
Keywords
Cite
@article{arxiv.math/9712256,
title = {Hopf Algebras and Edge-Labeled Posets},
author = {Nantel Bergeron and Frank Sottile},
journal= {arXiv preprint arXiv:math/9712256},
year = {2016}
}
Comments
LaTeX-2e, 9 pages. J. Algebra, to appear. Added examples, corrected typos, revised contents