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Coloring Complexes and Combinatorial Hopf Monoids

2016/11/13 by Jacob White, White, Jacob
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Category Theory (math.CT) #Combinatorics (math.CO) #FOS: Mathematics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1611.04079

openalex publication_date 2016/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the notion of a coloring complex of a graph to linearized combinatorial Hopf monoids. We determine when a linearized combinatorial Hopf monoid has such a construction, and discover some inequalities that are satisfied by the quasisymmetric function invariants associated to the combinatorial Hopf monoid. We show that the collection of all such coloring complexes forms a linearized combinatorial Hopf monoid, which is the terminal object in the category of combinatorial Hopf monoids with convex characters. We also study several examples of combinatorial Hopf monoids.

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