Spherical t-designs which are orbits of finite groups
ジャーナル
フリー
1984 年 36 巻 2 号 p. 341-354
詳細
- Published: 1984 Received: 1983/05/27 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
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訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文サブタイトル 訂正内容: Wrong : Dedicated to Professor Hirosi Nagao on the occasion of his 60-th birthday
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報 訂正内容: 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.
訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル 訂正内容: -
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