1984/06/01 by Paul H. Edelman · 1 citation
Engineering · Mathematics · #graph theory and CDMA systems #Graph theory and applications #Point processes and geometric inequalities #Mathematics #Hyperplane #Order (exchange) #Combinatorics #Pure mathematics
paper · doi:10.2307/1999150
openalex publication_date 1984/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/04
Abstract. We study a partial order on the regions of R " dissected by hyperplanes. This includes a computation of the Mobius function and, in some cases, of the homotopy type. Applications are presented to zonotopes, the weak Bruhat order on Weyl groups and acyclic orientations of graphs. 0. Introduction. Let % — 77,, H2,...,Hk] be a set of hyperplanes in R". Then the components of R " — UHe.xH form a set 9t of open n-cells we will call regions. Traditionally 9t has been studied in terms of enumeration, for instance counting the number of regions and the number of intersections of various dimensions among the hyperplanes in %. For a thorough discussion of this problem see Zaslavsky's