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Spherical t-designs which are orbits of finite groups
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1984 Volume 36 Issue 2 Pages 341-354
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- Published: 1984 Received: May 27, 1983 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Hirosi Nagao on the occasion of his 60-th birthday
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) E. Bannai, On some spherical t-designs, J. Combinatorial Theory (A), 26 (1979), 157-161.
2) E. Bannai, Orthogonal polynomials, algebraic combinatorics, and spherical t-designs, Proc. of Symp. in Pure Math., 37 (1980), 465-468.
3) E. Bannai and T. Ito, Algebraic Combinatorics, Part I, Association Schemes, Benjamin/Cummings Lecture Note Series in Math., 1984.
4) C. W. Curtis, W. M. Kantor and G. Seitz, The 2-transitive permutation representations of the finite Chevalley groups, Trans. Amer. Math. Soc., 218 (1976), 1-57.
5) P. Delsarte, An algebraic approach to the association schemes of coding theory, Philips Res. Repts. Suppi., 10 (1973).
6) P. Delshrte, J. M. Goethals and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata, 6 (1977), 263-288.
7) T. A. Dowling, On the orbit numbers of a finite geometric lattice, (preprint, Oct. 1981).
8) A. Erdélyi et al., Higher Transcendental Functions, Vol II, McGraw Hill, New York, 1953.
9) J. M. Goethals and J. J. Seidel, Spherical designs, Proc. of Symp. in Pure Math., 34 (1979), 255-272.
10) J. M. Goethals and J. J. Seidel, Cubature formulae, polytopes and spherical designs, Proc. Coxeter Symposium,(Toront, May 1979), in Geometric Vein, 203--218, Springer, 1982.
11) C. Hering, Transitive linear groups and linear groups which contain irreducible subgroups of prime order, II, to appear.
12) Y. Hong, On spherical t-designs in R2, European J. Combinatorics, 3 (1982), 255-258.
13) W. M. Kantor, k-homogeneous groups, Math. Z., 124 (1972), 261-265.
14) J. H. Lindsey, Jr., On a six dimensional projective representation of PSU4(3), Pacific J. Math., 36 (1971), 407-425.
15) D. Livingstone and A. Wagner, Transitivity of finite permutation groups on unordered sets, Math. Z., 90 (1965), 393-403.
16) F. D. Murnaghan, The Theory of Group Representations, Johns Hopkins Univ. Press, Baltimore, 1938.
17) P. M. Neumann, Generosity and characters of multiply transitive permutation groups, Proc. London Math. Soc., 31 (1975), 457-481.
18) R. Noda, Some inequalities for t-designs, Osaka J. Math., 13 (1976), 361-366.
19) D. K. Ray-Chaudhuri and R. M. Wilson, On t-designs, Osaka J. Math., 12 (1975), 737-744.
20) P. Seymour and T. Zaslavsky, Averaging sets. A generalization of mean values, and spherical designs, to appear in Advances in Math.
21) R. P. Stanley, Some aspects of groups acting on finite posets, J. Combinatorial Theory (A), 32 (1982), 132-161.
22) M. Takeuchi, Modern Spherical Function Theory, Iwanami Publ., Tokyo, 1975, (in Japanese).
23) H. Weyl, Classical Groups, Princeton Univ. Press, 1946.
24) A. Wolf, Spaces of Constant Curvature, McGraw Hill, New York, 1967.
25) D. Wright, The irreducible characters of the simple group of M. Suzuki of order 448, 345, 497, 600, J. Algebra, 29 (1974), 303-323.
26) S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978.
Right : [1] E. Bannai, On some spherical t-designs, J. Combinatorial Theory (A), 26 (1979), 157-161.
[2] E. Bannai, Orthogonal polynomials, algebraic combinatorics, and spherical t-designs, Proc. of Symp. in Pure Math., 37 (1980), 465-468.
[3] E. Bannai and T. Ito, Algebraic Combinatorics, Part I, Association Schemes, Benjamin/Cummings Lecture Note Series in Math., 1984.
[4] C. W. Curtis, W. M. Kantor and G. Seitz, The 2-transitive permutation representations of the finite Chevalley groups, Trans. Amer. Math. Soc., 218 (1976), 1-57.
[5] P. Delsarte, An algebraic approach to the association schemes of coding theory, Philips Res. Repts. Suppi., 10 (1973).
[6] P. Delshrte, J. M. Goethals and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata, 6 (1977), 263-288.
[7] T. A. Dowling, On the orbit numbers of a finite geometric lattice, (preprint, Oct. 1981).
[8] A. Erdélyi et al., Higher Transcendental Functions, Vol II, McGraw Hill, New York, 1953.
[9] J. M. Goethals and J. J. Seidel, Spherical designs, Proc. of Symp. in Pure Math., 34 (1979), 255-272.
[10] J. M. Goethals and J. J. Seidel, Cubature formulae, polytopes and spherical designs, Proc. Coxeter Symposium, (Toront, May 1979), in Geometric Vein, 203-218, Springer, 1982.
[11] C. Hering, Transitive linear groups and linear groups which contain irreducible subgroups of prime order, II, to appear.
[12] Y. Hong, On spherical t-designs in R2, European J. Combinatorics, 3 (1982), 255-258.
[13] W. M. Kantor, k-homogeneous groups, Math. Z., 124 (1972), 261-265.
[14] J. H. Lindsey, Jr., On a six dimensional projective representation of PSU4(3), Pacific J. Math., 36 (1971), 407-425.
[15] D. Livingstone and A. Wagner, Transitivity of finite permutation groups on unordered sets, Math. Z., 90 (1965), 393-403.
[16] F. D. Murnaghan, The Theory of Group Representations, Johns Hopkins Univ. Press, Baltimore, 1938.
[17] P. M. Neumann, Generosity and characters of multiply transitive permutation groups, Proc. London Math. Soc., 31 (1975), 457-481.
[18] R. Noda, Some inequalities for t-designs, Osaka J. Math., 13 (1976), 361-366.
[19] D. K. Ray-Chaudhuri and R. M. Wilson, On t-designs, Osaka J. Math., 12 (1975), 737-744.
[20] P. Seymour and T. Zaslavsky, Averaging sets. A generalization of mean values, and spherical designs, to appear in Advances in Math.
[21] R. P. Stanley, Some aspects of groups acting on finite posets, J. Combinatorial Theory (A), 32 (1982), 132-161.
[22] M. Takeuchi, Modern Spherical Function Theory, Iwanami Publ., Tokyo, 1975, (in Japanese).
[23] H. Weyl, Classical Groups, Princeton Univ. Press, 1946.
[24] A. Wolf, Spaces of Constant Curvature, McGraw Hill, New York, 1967.
[25] D. Wright, The irreducible characters of the simple group of M. Suzuki of order 448, 345, 497, 600, J. Algebra, 29 (1974), 303-323.
[26] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978.
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