Combinatorial Hopf Algebras of Simplicial Complexes
Abstract
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 combinatorial Hopf algebras give rise to symmetric functions that encode information about colorings of simplicial complexes and their -vectors. We also use characters to give a generalization of Stanley's -color theorem. A -analog version of this family of characters is also studied.
Keywords
Cite
@article{arxiv.1505.04458,
title = {Combinatorial Hopf Algebras of Simplicial Complexes},
author = {Carolina Benedetti and Joshua Hallam and John Machacek},
journal= {arXiv preprint arXiv:1505.04458},
year = {2016}
}
Comments
To appear in SIAM J. of Discrete Math. This version has new material, including a proof of the antipode formula. The even and odd subalgebras section is corrected. An extended abstract version of this article appeared in the Proceedings of FPSAC'15