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 language | English (US) |
|---|---|
| Pages (from-to) | 1-13 |
| Number of pages | 13 |
| Journal | Discrete and Computational Geometry |
| Volume | 23 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2000 |