On some Hopf monoids in graphical species

Details On some Hopf monoids in graphical species On some Hopf monoids in graphical species

2011-10-13

arxiv.org/abs/1110.3077v1

Mathematics

Combinatorics

18 pages, 8 commutative diagrams, 6 other figures

Scientific paper

Combinatorial Hopf algebras arise in a variety of applications. Recently, Aguiar and Mahajan showed how many well-studied Hopf algebras are closely related to Hopf monoids in species. In this paper, we study Hopf monoids in graphical species, giving a `graph-theoretic' analogue to the work of Aguiar and Mahajan. In particular, several examples of Hopf monoids in graphical species are detailed, most of which are related to graph coloring, or hyperplane arrangements associated to graphs.

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