Generalized Dehn-Sommerville relations for hypergraphs

The generalized Dehn-Sommerville relations determine the odd subalgebra of the combinatorial Hopf algebra. We introduce a class of eulerian hypergraphs that satisfy the generalized Dehn-Sommerville relations for the combinatorial Hopf algebra of hypergraphs. We characterize a wide class of eulerian hypergraphs in terms of the combinatorics of underlying clutters. The analogous results hold for simplicial complexes by the isomorphism which is induced by the correspondence between clutters and simplicial complexes.