  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.
