Orbits of the hyperoctahedral group as Euclidean designs

Journal of Algebraic Combinatorics

Volumn 25, Issue 4, 2007, Pages 375-397

  Bajnok, Béla ^a  

^a GETTYSBURG COLLEGE   (United States)

Author keywords

Euclidean design; Harmonic polynomial; Hyperoctahedral group; Spherical design; Tight design

Indexed keywords

BOUNDARY CONDITIONS; EQUATIONS OF STATE; HARMONIC ANALYSIS; POLYNOMIALS; VECTORS;

EUCLIDEAN DESIGNS; HYPEROCTAHEDRAL GROUP; HYPEROCTAHEDRON; INEQUALITY; SPHERICAL DESIGN; TIGHT DESIGN; WEYL GROUP;

NUMBER THEORY;

EID: 34247537189     PISSN: 09259899     EISSN: 15729192     Source Type: Journal    
DOI: 10.1007/s10801-006-0042-3     Document Type: Article

References (22)

1. B. Bajnok, "Construction of spherical t-designs," Geom. Dedicata 43/2 (1992), 167-179.
2. B. Bajnok, "On Euclidean designs," Adv. Geom. 6 (2006) 431-446.
3. Ei. Bannai, "On extremal finite sets in the sphere and other metric spaces," London Math. Soc. Lecture Note Ser. 131 (1988) 13-38.
4. Ei. Bannai and Et. Bannai, "On Euclidean tight 4-designs," Preprint.
5. Et. Bannai, "On antipodal Euclidean tight (2e + 1)-designs," Preprint.
6. J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices and Groups, 3rd ed. Springer-Verlag, 1999.
7. P. de la Harpe and C. Pache, "Cubature formulas, geometrical designs, reproducing kernels, and Markov operators," Preprint.
8. P. de la Harpe, C. Pache, and B. Venkov, "Construction of spherical cubature formulas using lattices," Preprint.
9. P. Delsarte, J.M. Goethals, and J.J. Seidel, "Spherical codes and designs," Geom. Dedicata 6/3 (1977) 363-388.
10. P. Delsarte and J.J. Seidel, "Fisher type inequalities for Euclidean t-designs," Linear Algebra Appl. 114-115 (1989), 213-230.
11. A. Erdélyi et al., Higher Transcendental Functions, (Bateman Manuscript Project), MacGraw-Hill, Vol. 2, 1953.
12. T. Ericson and V. Zinoviev, "Codes on Euclidean spheres," Elsevier, 2001.
13. C.D. Godsil, Algebraic Combinatorics, Chapman and Hall, Inc., 1993.
14. J.M. Goethals and J.J. Seidel, "Spherical designs," in Relations Between Combinatorics and Other Parts of Mathematics, Proc. Sympos. Pure Math., D.K. Ray-Chaudhuri (Ed.), Amer. Math. Soc., Providence, RI, 1979, vol. 34, pp. 255-272.
15. J.M. Goethals and J.J. Seidel, "Cubature formulae, polytopes and spherical designs," in The Geometric Vein: The Coxeter Festschrift, C. Davis, B. Grünbaum, and F.A. Sher (Eds.), Springer-Verlag, New York-Berlin, 1981, pp. 203-218.
16. F.B. Hildebrand, Introduction to Numerical Analysis, 2nd ed. McGraw-Hill, Inc., 1974.
17. A. Neumaier and J.J. Seidel, "Discrete measures for spherical designs, eutactic stars and lattices," Nederl. Akad. Wetensch. Indag. Math. 50/3 (1988), 321-334.
18. J.J. Seidel, "Designs and approximation," Contemp. Math. 111 (1990), 179-186.
19. J.J. Seidel, "Isometric embeddings and geometric designs," Discrete Math. 136 (1994), 281-293.
20. J.J. Seidel, "Spherical designs and tensors," in Progress in algebraic combinatorics, Adv. Stud. Pure Math., E. Bannai and A. Munemasa (Eds.), Math. Soc. Japan, Tokyo, 1996, vol. 24, pp.309-321.
21. P.D. Seymour and T. Zaslavsky, "Averaging sets: A generalization of mean values and spherical designs," Adv. Math. 52 (1984), 213-240.
22. A.H. Stroud, Approximate Calculation of Multiple Integrals, Prentice-Hall, Inc., 1971.