Max Hlavacek: Dehn-Sommerville Equations for Eulerian Cubical Complexes
Abstract
The classical Dehn--Sommerville equations, relating the
face numbers of simplicial polytopes, have an analogue for cubical polytopes.
These relations can be generalized to apply to simplicial and cubical Eulerian
complexes. In this talk, we will introduce a few different known proofs of the
classical Dehn--Sommerville relations for simplicial complexes, relating this
result to concepts such as zeta polynomials of posets, Ehrhart polynomials of
simplicial complexes, and chain-partitions of posets. We will then discuss whether
each proof idea can be adapted to the cubical case.