Combinatorica

, Volume 3, Issue 2, pp 147–152

An upper bound for the cardinality of ans-distance subset in real euclidean space, II

  • Eiichi Bannai
  • Etsuko Bannai
  • Dennis Stanton
Article

Abstract

It is shown that ifX is ans-distance subset inRd, then |X|≦(sd+s).

AMS subject classification (1980)

05 B 99 51 M 99 

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References

  1. [1]
    E. Bannai andE. Bannai, An upper bound for the cardinality of ans-distance subset in real Euclidean space,Combinatorica 1 (1981), 99–102.MATHMathSciNetGoogle Scholar
  2. [2]
    A. Blokhuis, A new upper bound for the cardinality of 2-distance sets in Euclidean space,Eindhoven Univ. of Technology, Memorandum 1981—04, Feb. 1981.Google Scholar
  3. [3]
    A. Blokhuis, An upper bound for the cardinality ofs-distance sets inE d andH d,Eindhoven Univ. Techn. Memorandum 1982-68, May 1982. (This is also part of his Ph. D. Thesis entitled “Few distance sets”, 1983.)Google Scholar
  4. [4]
    E. W. Hobson,The Theory of Spherical and Ellipsoidal Harmonics, Cambridge, 1931.Google Scholar
  5. [5]
    D. G. Larman, C. A. Rogers andJ. J. Seidel, On two-distance sets in Euclidean space,Bull. London Math. Soc. 9 (1977), 261–267.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Akadémiai Kiadó 1983

Authors and Affiliations

  • Eiichi Bannai
    • 1
  • Etsuko Bannai
    • 1
  • Dennis Stanton
    • 2
  1. 1.Department of MathematicsThe Ohio State UniversityColumbusU.S.A.
  2. 2.School of MathematicsThe University of MinnesotaMinneapolisU.S.A.

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