Authors
Citation
C. Ahrens et al., Convexity and the beta invariant, DISC COM G, 22(3), 1999, pp. 411-424
Citations number
11
Categorie Soggetti
Engineering Mathematics
Journal title
DISCRETE & COMPUTATIONAL GEOMETRY
ISSN journal
01795376
→ ACNP
Volume
22
Issue
3
Year of publication
1999
Pages
411 - 424
Database
ISI
SICI code
0179-5376(199910)22:3<411:CATBI>2.0.ZU;2-5
Abstract
We apply a generalization of Crapo's beta invariant to finite subsets of R-
n. For a finite subset C of the plane, we prove beta(C) = \int(C)\, where \
int(C)\ is the number of interior points of C, i.e., the number of points o
f C which are not on the boundary of the convex hull of C. This gives the f
ollowing formula: Sigma(K free)(-1)(\K\-1)\K\ = \int(C)\.