Séminaire Lotharingien de Combinatoire, 82B.32 (2019), 12 pp.
Jean-Christophe Aval, Théo Karaboghossian, and Adrian Tanasa
Polynomial invariants and reciprocity theorems for the Hopf monoid of hypergraphs and its sub-monoids
Abstract.
In arXiv:1709.07504 Aguiar and Ardila 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.
Received: November 15, 2018.
Accepted: February 17, 2019.
Final version: April 1, 2019.
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