Carolina Benedetti ; Joshua Hallam ; John Machacek - Combinatorial Hopf Algebras of Simplicial Complexes

dmtcs:2506 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) - https://doi.org/10.46298/dmtcs.2506
Combinatorial Hopf Algebras of Simplicial Complexes

Authors: Carolina Benedetti 1; Joshua Hallam 1; John Machacek ORCID-iD1

  • 1 Department of Mathematics [Lansing]

We consider a Hopf algebra of simplicial complexes and provide a cancellation-free formula for its antipode. We then obtain a family of combinatorial Hopf algebras by defining a family of characters on this Hopf algebra. The characters of these Hopf algebras give rise to symmetric functions that encode information about colorings of simplicial complexes and their $f$-vectors. We also use characters to give a generalization of Stanley’s $(-1)$-color theorem.


Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Imported on: November 21, 2016
Keywords: Combinatorial Hopf algebra,quasi-symmetric functions,simplicial complex,colorings,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

Linked publications - datasets - softwares

Source : ScholeXplorer IsRelatedTo DOI 10.1006/aima.1995.1020
  • 10.1006/aima.1995.1020
A Symmetric Function Generalization of the Chromatic Polynomial of a Graph

Consultation statistics

This page has been seen 246 times.
This article's PDF has been downloaded 333 times.