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

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Applications of Fibonacci Numbers

Abstract

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

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References

  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.

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  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.

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  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.

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  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.

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  7. Hoggatt, V.E., Jr. and Hansell, W. “The Hidden Hexagon Squares”. The Fibonacci Quarterly, Vol. 9 (1971): pp. 120–133.

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  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.

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  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.

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  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.

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  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.

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© 1996 Kluwer Academic Publishers

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Ando, S., Sato, D. (1996). Multiple Color Version of the Star of David Theorems on Pascal’s Triangle and Related Arrays of Numbers. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0223-7_3

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  • DOI: https://doi.org/10.1007/978-94-009-0223-7_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6583-2

  • Online ISBN: 978-94-009-0223-7

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