On posets and hopf algebras

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127 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)1-25
Number of pages25
JournalAdvances in Mathematics
Volume119
Issue number1
DOIs
StatePublished - Apr 15 1996

Bibliographical note

Funding Information:
* The author began this work at MIT and continued it at UQAM. This research is supported by CRM, Universite de Montreal and LACIM, Universite du Quebec a Montreal.

ASJC Scopus subject areas

  • General Mathematics

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