On equivariant generalization of Dehn-Sommerville equations

Abstract

We consider an action of combinatorial automorphism on a triangulation of a sphere and obtain some relations satisfied by invariant faces. In the case of identity automorphism these relations appear to be the Dehn-Sommerville equations. Our result follows from the general consideration of an action of a finite group on a graded module and, in particular, on a Gorenstein module. Several examples are given.