2020/10/27 by Marcelo Aguiar, Aguiar, Marcelo, Jose Bastidas +1
Computer Science · Mathematics · #05Exx #18M80 (primary) 13F25 (secondary) #52Bxx #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2010.14283
openalex publication_date 2020/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the Hopf monoid of sets of cycles and paths, which contains the Faà di Bruno Hopf monoid as a submonoid. We give cancellation-free and grouping-free formulas for its antipode, one in terms of tubings and one in terms of pointed noncrossing partitions. We provide an explicit description of the group of characters of this Hopf monoid in terms of pairs of power series. Using graph associahedra, we relate paths and cycles to associahedra and cyclohedra, respectively. We give formulas for inversion in the group of characters in terms of the faces of these polytopes.