Generalizations of Eulerian partially ordered sets, flag numbers, and the Mobius function [article]

Margaret M. Bayer, Gabor Hetyei
2001 arXiv   pre-print
A partially ordered set is r-thick if every nonempty open interval contains at least r elements. This paper studies the flag vectors of graded, r-thick posets and shows the smallest convex cone containing them is isomorphic to the cone of flag vectors of all graded posets. It also defines a k-analogue of the Mobius function and k-Eulerian posets, which are 2k-thick. Several characterizations of k-Eulerian posets are given. The generalized Dehn-Sommerville equations are proved for flag vectors
more » ... k-Eulerian posets. A new inequality is proved to be valid and sharp for rank 8 Eulerian posets.
arXiv:math/0101075v1 fatcat:tfoxlbvievfl5fa7qkmunpyzau