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arXiv · 1904.09878

Polynomial invariants and reciprocity theorems for the Hopf monoid of hypergraphs and its sub-monoids

Jean-Christophe Aval·Théo Karaboghossian·Adrian Tanasa
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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.

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Jean-Christophe Aval, Théo Karaboghossian, Adrian Tanasa. 2019-04-19. Polynomial invariants and reciprocity theorems for the Hopf monoid of hypergraphs and its sub-monoids. https://arxiv.org/abs/1904.09878

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