The Hopf monoid of hypergraphs and its sub-monoids: basic invariant and reciprocity theorem

Autor:	Aval, Jean-Christophe, Karaboghossian, Théo, Tanasa, Adrian
Rok vydání:	2018
Předmět:	Mathematics - Combinatorics 05E99 05C15 05C65
Zdroj:	The Electronic Journal of Combinatorics, Volume 27, Issue 1 (2020) P1.34
Druh dokumentu:	Working Paper
DOI:	10.37236/8740
Popis:	In arXiv:1709.07504 Ardila and Aguiar give a Hopf monoid structure on hypergraphs as well as a general construction of polynomial invariants on Hopf monoids. Using these results, we define in this paper a new polynomial invariant on hypergraphs. We give a combinatorial interpretation of this invariant on negative integers which leads to a reciprocity theorem on hypergraphs. Finally, we use this invariant to recover well-known invariants on other combinatorial objects (graphs, simplicial complexes, building sets etc) as well as the associated reciprocity theorems. Comment: 18 pages, 5 figures. Minor changes. Accepted for publication in the Electronic Journal of Combinatorics
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1806.08546 Zobrazit plný text záznamu View this record from Arxiv