2011/10/13 by Jacob A. White, White, Jacob A.
Computer Science · Mathematics · #05C99 #16T30 #18D10 #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Category Theory (math.CT) #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Quantum Algebra (math.QA) #math.CO #math.CT #math.QA #msc:05C99 #msc:16T30 #msc:18D10
paper · pdf · doi:10.48550/arxiv.1110.3077
18 pages, 8 commutative diagrams, 6 other figures
arxiv created 2011/10/13 · openalex publication_date 2011/10/13 · arxiv updated 2011/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.