Convexity and the Beta Invariant

Convexity and the Beta Invariant

We apply a generalization of Crapo's beta invariant to finite subsets of R super(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 of C which are not on the boundary of the convex hull of C . Th...

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Veröffentlicht in:Discrete & computational geometry 1999-10, Vol.22 (3), p.411-424
Hauptverfasser: Ahrens, C., Gordon, G., McMahon, E. W.
Format: Artikel
Sprache:eng
Schlagworte:
Boundaries
Computational geometry
Convexity
Hulls (structures)
Invariants
Mathematical analysis
Planes
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Zusammenfassung:We apply a generalization of Crapo's beta invariant to finite subsets of R super(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 of C which are not on the boundary of the convex hull of C . This gives the following formula: capital sigma sub(K free) (-1) |K|-1 |K|=|int(C)|.
ISSN:0179-5376
1432-0444
DOI:10.1007/PL00009469