论文信息 - Upper Bounds on the Maximal Number of Facets of 0/1-Polytopes

Upper Bounds on the Maximal Number of Facets of 0/1-Polytopes

We prove two new upper bounds on the number of facets that a d -dimensional 0/1-polytope can have. The first one is 2(d? 1)!+ 2(d? 1) (which is the best one currently known for small dimensions), while the second one of O((d? 2)!) is the best known bound for large dimensions.

Günter Rote | Volker Kaibel | Tamás Fleiner

[1] Imre Bárány,et al. The convex hull of the integer points in a large ball , 1998 .

[2] George E. Andrews. An asymptotic expression for the number of solutions of a general class of Diophantine equations , 1961 .

[3] Günter M. Ziegler,et al. Extremal Properties of 0/1-Polytopes , 1997, Discret. Comput. Geom..

[4] Oswin Aichholzer,et al. Extremal Properties of 0/1-Polytopes of Dimension 5 , 2000 .

[5] Vojtěch Jarník,et al. Über die Gitterpunkte auf konvexen Kurven , 1926 .

[6] Jovisa D. Zunic,et al. On the Maximal Number of Edges of Convex Digital Polygons Included into an m x m -Grid , 1995, J. Comb. Theory A.

[7] G. Ziegler. Lectures on Polytopes , 1994 .

[8] Wolfgang M. Schmidt,et al. Integer points on curves and surfaces , 1985 .

[9] Attila Pór,et al. On 0-1 Polytopes with Many Facets , 2001 .

[10] S. V. Konyagin,et al. A bound, in terms of its volume, for the number of vertices of a convex polyhedron when the vertices have integer coordinates , 1984 .

[11] V. I. Arnol'd,et al. Statistics of integral convex polygons , 1980 .

[12] George E. Andrews,et al. A LOWER BOUND FOR THE VOLUME OF STRICTLY CONVEX BODIES WITH MANY BOUNDARY LATTICE POINTS , 1963 .