Seminar

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.