Lower bounds for measurable chromatic numbers

Geometric and Functional Analysis

Volumn 19, Issue 3, 2009, Pages 645-661

  Bachoc, Christine ^a   Nebe, Gabriele ^b   de Oliveira Filho, Fernando Mário ^c   Vallentin, Frank ^d  

^a UNIVERSITÉ BORDEAUX 1   (France)

^b RWTH AACHEN UNIVERSITY   (Germany)

^c CWI   (Netherlands)

^d DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Measurable chromatic number; Nelson Hadwiger problem; Orthogonal polynomials; Semidefinite programming; Spherical codes

Indexed keywords

EID: 84905011444     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-009-0013-7     Document Type: Article

References (24)

1. [AAR] G. E. Andrews, R. Askey, R. Roy, Special Functions, Cambridge University Press, 1999.
2. [B] C. Bachoc, Linear programming bounds for codes in Grassmannian spaces, IEEE Trans. Inf. Th. 52 (2006), 2111-2125.
3. [Bo] S. Bochner, Hilbert distances and positive definite functions, Ann. of Math. 42 (1941), 647-656.
4. [BrE] N. G. de Bruijn, P. Erdo{double acute}s, A colour problem for infinite graphs and a problem in the theory of relations, Indagationes Math. 13 (1951), 369-373.
5. [D] P. Delsarte, An Algebraic Approach to the Association Schemes of Coding Theory, Philips Res. Rep. Suppl., 1973.
6. [DGS] P. Delsarte, J. M. Goethals, J. J. Seidel, Spherical codes and designs, Geom. Dedicata 6 (1977), 363-388.
7. n, J. Combin. Theory Ser. A 31 (1981), 187-189.
8. [FrR] P. Frankl, V. Rödl, Forbidden intersections, Trans. Amer. Math. Soc. 300 (1987), 259-286.
9. [FrW] P. Frankl, R. M. Wilson, Intersection theorems with geometric consequences, Combinatorica 1 (1981), 357-368.
10. [KL] G. A. Kabatiansky, V. I. Levenshtein, Bounds for packings on a sphere and in space, Problems of Information Transmission 14 (1978), 1-17.
11. [Kn] D. E. Knuth, The Sandwich Theorem, Electron. J. Combin. 1 (1994).
12. [LR] D. G. Larman, C. A. Rogers, The realization of distances within sets in Euclidean space, Mathematika 19 (1972), 1-24.
13. [L1] L. Lovász, On the Shannon capacity of a graph, IEEE Trans. Inf. Th. 25 (1979), 1-7.
14. [L2] L. Lovász, Self-dual polytopes and the chromatic number of distance graphs on the sphere, Acta Sci. Math. 45 (1983), 317-323.
15. [MRR] R. J. McEliece, E. R. Rodemich, H. C. Rumsey Jr., TheLovász bound and some generalizations, J. Combin. Inf. System Sci. 3 (1978) 134-152.
16. n, J. Eur. Math. Soc., toappear.
17. [R] A. M. Raigorodskii, On the chromatic number of a space, Uspekhi Mat. Nauk 55 (2000), 147-148.
18. [S] I. J. Schoenberg, Positive definite functions on spheres, Duke Math. J. 9 (1942), 96-108.
19. [Sc] A. Schrijver, A comparison of the Delsarte and Lovász bounds, IEEE Trans. Inf. Th. 25 (1979), 425-429.
20. [Sz] G. Szegö, Orthogonal Polynomials, Volume XXIII, Colloqium Publications, American Mathematical Society, 1967.
21. [Szé] L. A. Székely, Erdo{double acute}s on unit distances and the Szemerédi-Trotter theorems, in Paul Erdo{double acute}s and His Mathematics (G. Halász, L. Lovász, M. Simonovits, V. T. Sós, eds.), Springer, (2002), 649-666.
22. n, Discrete Math. 75 (1989), 343-372.
23. [VK] N. Ja. Vilenkin, A. U. Klimyk, Representation of Lie Groups and Special Functions, Vol. 2, Kluwer Academic Publishers, 1993.
24. [W] G. N. Watson, A Treatise on the Theory of Bessel Function, Cambridge Mathematical Library, 1995.