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Pascal’s Triangle: Top Gun or Just One of the Gang?

In: Applications of Fibonacci Numbers

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  • Daniel C. Fielder
  • Cecil O. Alford

Abstract

Pascal’s triangle can appear as a member of classes of triangular arrays where presumably no class member should be ranked in importance over any other. Two such cases which came to mind were the multinomial triangles [6] and the Hoggatt triangles [2]. No doubt there are others. We selected the multinomial triangles. Was Pascal’s triangle only a binomial triangle in a sea of trinomial, quadrinomial, pentanomial, etc., triangles, or might it exhibit a significant influence on the makeup of the other multinomial triangles? We admit a certain prejudice in our choice. Computer experimentation with partition counting, large multinomial expansions, and generating functions using computer algebra systems (muMath, Derive, Mathematica) hinted at a definite Pascal influence. A few years ago, such experimentation would have been virtually impossible.

Suggested Citation

  • Daniel C. Fielder & Cecil O. Alford, 1991. "Pascal’s Triangle: Top Gun or Just One of the Gang?," Springer Books, in: G. E. Bergum & A. N. Philippou & A. F. Horadam (ed.), Applications of Fibonacci Numbers, pages 77-90, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-3586-3_10
    DOI: 10.1007/978-94-011-3586-3_10
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