Generalizations of Eulerian partially ordered sets, flag numbers, and the Mobius function
Combinatorics
2007-05-23 v1
Abstract
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 of k-Eulerian posets. A new inequality is proved to be valid and sharp for rank 8 Eulerian posets.
Cite
@article{arxiv.math/0101075,
title = {Generalizations of Eulerian partially ordered sets, flag numbers, and the Mobius function},
author = {Margaret M. Bayer and Gabor Hetyei},
journal= {arXiv preprint arXiv:math/0101075},
year = {2007}
}