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

European Journal of Combinatorics

Volumn 21, Issue 1, 2000, Pages 121-130

  Fleiner, Tamás ^a   Kaibel, Volker ^b   Rote, Günter ^c  

^a CWI   (Netherlands)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^c FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034380090     PISSN: 01956698     EISSN: None     Source Type: Journal    
DOI: 10.1006/eujc.1999.0326     Document Type: Article

References (16)

1. D. M. Acketa and J. D. Žunić, On the maximal number of edges of convex digital polygons included into an m x m-grid, J. Comb. Theory, Ser. A, 69 (1995), 358-368.
2. O. Aichholzer, Extremal properties of 0/1-polytopes of dimension 5, SFB Report 132, Technische Universität Graz, 1998, To appear in: Polytopes - Combinatorics and Computation, DMV-Seminars, G. Kalai and G. M. Ziegler (eds), Birkhäuser-Verlag, Basel.
3. G. E. Andrews, An asymptotic expression for the number of solutions of a general class of Diophantine equations, Trans. Am. Math. Soc., 99 (1961), 272-277.
4. G. E. Andrews, A lower bound for the volume of strictly convex bodies with many boundary lattice points, Trans. Am. Math. Soc., 106 (1963), 270-279.
5. V. I. Arnol'd, Statistics of integral convex polygons (in Russian), Funktsionalnyǐ Analiz i ego Prilozheniya, 14 (1980), no. 2, 1-3. English translation: Funct. Anal. Appl., 14 (1980), 79-81.
6. V. I. Arnol'd, Statistics of integral convex polygons (in Russian), Funktsionalnyǐ Analiz i ego Prilozheniya, 14 (1980), no. 2, 1-3. English translation: Funct. Anal. Appl., 14 (1980), 79-81.
7. I. Bárány and D. G. Larman, The convex hull of the integer points in a large ball, Math. Annalen, 312 (1998), 167-181.
8. T. Christof, SMAPO - 'Small' 0/1-polytopes in Combinatorial Optimization. World-Wide-Web page, http: //www.iwr.uni-heidelberg.de/iwr/comopt/soft/SMAPO/SMAPO.html, July, 1997.
9. V. Jarník, Über die Gitterpunkte auf konvexen Kurven, Math. Z., 24 (1926), 500-518.
10. S. V. Konyagin and K. A. Sevast'yanov, A bound, in terms of its volume, for the number of vertices of a convex polyhedron when the vertices have integer coordinates (in Russian), Funktsionalnyǐ Analiz i ego Prilozheniya, 18 (1984), no. 1, 13-15. English translation: Funct. Anal. Appl., 18 (1984), 11-13.
11. S. V. Konyagin and K. A. Sevast'yanov, A bound, in terms of its volume, for the number of vertices of a convex polyhedron when the vertices have integer coordinates (in Russian), Funktsionalnyǐ Analiz i ego Prilozheniya, 18 (1984), no. 1, 13-15. English translation: Funct. Anal. Appl., 18 (1984), 11-13.
12. U. Kortenkamp, 0/1-Polytopes with many facets. World-Wide-Web page, http://www.math. tu-berlin.de/~lmnd/01-Olympics.html, 1997.
13. U. Kortenkamp, Jürgen Richter-Gebert, Aravamuthan Sarangarajan and Günter M. Ziegler, Extremal properties of 0/1-polytopes, Discrete Comput. Geom., 17 (1997), 439-448.
14. W M. Schmidt, Integer points on curves and surfaces, Monatsh. Math., 99 (1985), 45-72.
15. T. Thiele, Extremalprobleme für Punktmengen, Diplomarbeit, Institut für Informatik, Freie Universität Berlin, 1991.
16. G. M. Ziegler, Lectures on Polytopes, Graduate Texts in Mathematics, 152, Springer-Verlag, New York, 1995 (revised printing, 1998).