✦ LIBER ✦

On Posets and Hopf Algebras

✍ Scribed by Richard Ehrenborg

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 810 KB
Volume: 119
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.1996.0026

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✦ Synopsis

We generalize the notion of the rank-generating function of a graded poset. Namely, by enumerating different chains in a poset, we can assign a quasi-symmetric function to the poset. This map is a Hopf algebra homomorphism between the reduced incidence Hopf algebra of posets and the Hopf algebra of quasi-symmetric functions. This work implies that the zeta polynomial of a poset may be viewed in terms Hopf algebras. In the last sections of the paper we generalize the reduced incidence Hopf algebra of posets to the Hopf algebra of hierarchical simplicial complexes.

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