Projections, shellings and duality

Details Projections, shellings and duality Projections, shellings and duality

2001-10-08

arxiv.org/abs/math/0110079v2

Mathematics

Combinatorics

Scientific paper

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 $h$ vector. The former may be regarded as a $q$-analogue of the Dehn-Sommerville equations. We also briefly discuss the connection with the random walks introduced by Bidigare, Hanlon and Rockmore.

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