Multiple Color Version of the Star of David Theorems on Pascal’s Triangle and Related Arrays of Numbers

  • Shiro Ando
  • Daihachiro Sato

Abstract

This paper deals with research results which are a continuation of the reports given in [2], [3], [8], [10] and [11].

Keywords

Convex Hull Binomial Coefficient Regular Hexagon Multiple Color Greatest Common Divisor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Ando, S. “A Triangular Array with Hexagon property, Dual to Pascal’s Triangle”. Applications of Fibonacci Numbers, Volume 2. Edited by G.E. Bergum, A.N. Philippou and A.F. Iloradam. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988, pp. 61–67.Google Scholar
  2. [2]
    Ando, S. and Sato, D. “Translatable and Rotatable Configurations which Give Equal Product, Equal GCD and Equal LCM Properties Simultaneously”. Applications of Fibonacci Numbers. Volume 3. Edited by G.E. Bergum, A.N. Philippou and A.F. Horadam. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1990, pp. 15–26.CrossRefGoogle Scholar
  3. [3]
    Ando, S. and Sato, D. “On the Proof of GCD and LCM Equalities Concerning the Generalized Binomial and Multinomial Coefficients”. Applications of Fibonacci Numbers. Volume 4. Edited by G.E. Bergum, A.N. Philippou and A.F. Horadam. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991, pp. 9–16.CrossRefGoogle Scholar
  4. [4]
    Gordon, B., Sato, D. and Straus, E.G. “Binomial Coefficients whose Products are Perfect Ar-th Powers”. Pacific J. Math., Vol. 118 (1985): pp. 393–400.MathSciNetMATHGoogle Scholar
  5. [5]
    Gould, H.W. “A New Greatest Common Divisor Property of the Binomial Coefficients”. The Fibonacci Quarterly, Vol. 10 (1972): pp. 565–568, 598.MathSciNetGoogle Scholar
  6. [6]
    Hillman, A.P. and Hoggatt, V.E., Jr. “A Proof of Gould’s Pascal Hexagon Conjecture”. The Fibonacci Quarterly, Vol. 10 (1972): pp. 565–568, 598.MathSciNetGoogle Scholar
  7. [7]
    Hoggatt, V.E., Jr. and Hansell, W. “The Hidden Hexagon Squares”. The Fibonacci Quarterly, Vol. 9 (1971): pp. 120–133.Google Scholar
  8. [8]
    Sato, D. and Ando, S. “Approximation Theorems of m-color Patterns by Translatable Simultaneous Equality Configurations on Pascal’s Triangle”. ICM 90 Abstract, Twenty First International Congress of Mathematicians, Kyoto Japan,, August (1990): p. 227.Google Scholar
  9. [9]
    Sato, D. and Hitotumatu, S. “Simple Proof that a p-adic Pascal’s Triangle is 120 Degree Rotatable”. Proceedings of the American Mathematical Society, Vol. 59 (1976): pp. 406–407.MathSciNetMATHGoogle Scholar
  10. [10]
    Ando, S. and Sato, D. “A Necessary and Sufficient Condition that Rays of a Star Configuration on Pascal’s Triangle Cover Its Center with Respect to GCD and LCM”. Applications of Fibonacci Numbers, Volume 5. Edited by G.E. Bergum, A.N. Philippou and A.F. Horadam. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993, pp. 11–36.CrossRefGoogle Scholar
  11. [11]
    Ando, S. and Sato, D. “On the Minimal Center Covering Stars with Respect to GCD in Pascal’s Pyramid and Its Generalizations”. Applications of Fibonacci Numbers. Volume 5. Edited by G.E. Bergum, A.N. Philippou and A.F. Horadam. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993, pp. 37–43.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Shiro Ando
  • Daihachiro Sato

There are no affiliations available

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