How neighborly can a centrally symmetric polytope be?

Discrete and Computational Geometry

Volumn 36, Issue 2, 2006, Pages 273-281

  Linial, Nathan ^a   Novik, Isabella ^b  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746923055     PISSN: 01795376     EISSN: 14320444     Source Type: Journal    
DOI: 10.1007/s00454-006-1235-1     Document Type: Article

References (20)

1. M. Aigner and G. M. Ziegler, Proofs from THE BOOK, third edition, Springer-Verlag, Berlin, 2004.
2. K. Ball, An elementary introduction to modern convex geometry, in Flavors of Geometry, pp. 1-58, Mathematical Sciences Research Institute Publication, 31, Cambridge University Press, Cambridge, 1997.
3. G. R. Burton, The nonneighbourliness of centrally symmetric convex polytopes having many vertices, J. Combin. Theory Ser. A 58 (1991), 321-322.
4. B. Carl and I. Stephani, Entropy, Compactness and the Approximation of Operators, Cambridge Tracts in Mathematics, 98, Cambridge University Press, Cambridge, 1990.
5. L. Danzer and B. Grünbaum, Über zwei Probleme bezüglich konvexer Körper von P. Erdös und von V. L. Klee, Math. Z. 79 (1962), 95-99.
6. D. L. Donoho, High-dimensional centrosymmetric polytopes with neighborliness proportional to dimension, available from http://www-stat. stanford.edu/~donoho/reports.html.
7. A. Yu. Garnaev and E. D. Gluskin, The widths of a Euclidean ball (in Russian), Dokl. Akad. Nauk SSSR 277(5) (1984), 1048-1052.
8. (English translation: Soviet Math. Dokl. 30(1) (1984), 200-204.)
9. B. Grünbaum, Convex Polytopes, second edition (prepared and with a preface by V. Kaibel, V. Klee, and G. M. Ziegler), Graduate Texts in Mathematics, 221, Springer-Verlag, New York, 2003.
10. E. R. Halsey, Zonotopal complexes on the d-cube, Doctoral dissertation, University of Washington (1972).
11. B. S. Kašin, The widths of certain finite-dimensional sets and classes of smooth functions (in Russian), Izv. Akad. Nauk SSSR Sci: Mat. 41(2) (1977), 334-351, 478.
12. (English translation: Math. USSR-Izv. 11(2) (1977), 317-333.)
13. Y. Makovoz, A simple proof of an inequality in the theory of n-widths, in Constructive Theory of Functions (Varna, 1987), pp. 305-308, Publ. House Bulgar. Acad. Sci., Sofia, 1988.
14. P. McMullen and G. C. Shephard, Diagrams for centrally symmetric polytopes, Mathematika 15 (1968), 123-138.
15. 1-Approximation, Cambridge Tracts in Mathematics, 93, Cambridge University Press, Cambridge, 1989.
16. M. Rudelson and R. Vershynin, Geometric approach to error correcting codes and reconstruction of signals, Int. Math. Res. Not. 64 (2005), 4019-4041.
17. R. Schneider, Neighbourliness of centrally symmetric polytopes in high dimensions, Mathematika 22(2) (1975), 176-181.
18. 1, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astmnom. Phys. 26 (1978), 691-694.
19. 1- Minimization: Go Over or Under?, Tech. Rep. TR05-09, Rice University, 2005.
20. G. M. Ziegler, Lectures on Polytopes, Graduate Texts in Mathematics, 152, Springer-Verlag, New York, 1995.