Projections, shellings and duality

Swapneel Mahajan

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arXiv · math/0110079

Projections, shellings and duality

Swapneel Mahajan

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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{ö}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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Swapneel Mahajan. 2001-10-08. Projections, shellings and duality. https://arxiv.org/abs/math/0110079

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