2001/10/08 by Swapneel Mahajan, Mahajan, Swapneel
Computer Science · Mathematics · #06A08 #52B22 #52B30 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.CO #math.GT #msc:06A08 #msc:52B22 #msc:52B30
paper · pdf · doi:10.48550/arxiv.math/0110079
arxiv created 2001/10/08 · openalex publication_date 2001/10/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Björner. 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.