Benedetti, Carolina and Hallam, Joshua and Machacek, John
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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.