Projections, shellings and duality
Combinatorics
2009-09-25 v2 Geometric Topology
Abstract
Projection maps which appear in the theory of buildings and oriented matroids are closely related to the notion of shellability. This was first observed by Bj{\"o}rner. In this paper, we give an axiomatic treatment of either concept and show their equivalence. We also axiomatize duality in this setting. As applications of these ideas, we prove a duality theorem on buildings and give a geometric interpretation of the flag vector. The former may be regarded as a -analogue of the Dehn-Sommerville equations. We also briefly discuss the connection with the random walks introduced by Bidigare, Hanlon and Rockmore.
Keywords
Cite
@article{arxiv.math/0110079,
title = {Projections, shellings and duality},
author = {Swapneel Mahajan},
journal= {arXiv preprint arXiv:math/0110079},
year = {2009}
}