Counting the Interior of a Point Configuration
نویسنده
چکیده
We prove a formula conjectured by Ahrens, Gordon, and McMa-hon for the number of interior points for a point connguration in R d. Our method is to show that the formula can be interpreted as a sum of Euler characteristics of certain complexes associated with the point connguration, 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.
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