Counting the interior points of a point configuration

P. H. Edelman, V. Reiner

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

We prove a formula conjectured by Ahrens, Gordon, and McMahon for the number of interior points for a point configuration in ℝd. Our method is to show that the formula can be interpreted as a sum of Euler characteristics of certain complexes associated with the point configuration, and then compute the homology of these complexes. This method extends to other examples of convex geometries. We sketch these applications, replicating an earlier result of Gordon, and proving a new result related to ordered sets.

Original languageEnglish (US)
Pages (from-to)1-13
Number of pages13
JournalDiscrete and Computational Geometry
Volume23
Issue number1
DOIs
StatePublished - Jan 2000

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