## Benedetti, Carolina and Hallam, Joshua and Machacek, John - 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)
Combinatorial Hopf Algebras of Simplicial Complexes

Authors: Benedetti, Carolina and Hallam, Joshua and Machacek, John

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.

Source : oai:HAL:hal-01337756v1
Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Submitted on: November 21, 2016
Keywords: Combinatorial Hopf algebra,quasi-symmetric functions,simplicial complex,colorings,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]