Cycles of binomial coefficients

A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 14, 2008, Number 3, Pages 19—24
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Authors and affiliations

A. G. Shannon
Warrane College, The University of New South Wales, Kensington 1465, &
Raffles College, 99 Mount Street, North Sydney, NSW 2065, Australia

Absrtacts

This paper considers some properties of rising and falling factorials by analogy with some classic results in number theory for cycles of binomial coefficients.

Keywords

  • Rising and falling factorials
  • Binomial coefficients
  • Legendre polynomial

AMS Classification

  • 11B65
  • 11B39
  • 05A30

References

  1. Carltiz, L. Note on a q-identity. Mathematica Scandinavica. 3(1955): 281-282.
  2. Carlitz, L. Some Congruences Involving Sums of Binomial Coefficients. Duke Mathematical Journal. 27 (1960): 77-79.
  3. Carlitz, L. Congruence Properties of Certain Linear Homogeneous Difference Equations. Acta Arithmetica. 7 (1962): 173:186.
  4. Carlitz, L. Sums of products of Multinomial Coefficients. Elemente der Mathematik. 18 (1963): 37-39.
  5. Carlitz, L. Some Multiple Sums and Binomial Identities. Journal of the Society of Industrial and Applied Mathematics. 13 (1965): 469-486.
  6. Carlitz, L. Multiple Sums and Generating Functions. Collectanea Mathematica. 17 (1965): 281-296.
  7. Carlitz, L. Rectangular Arrays and Plane Partitions. Acta Arithmetica. 13 (1967): 29-47.
  8. Carlitz, L. A Binomial Identity. SIAM Review. 9 (1967): 229-231.
  9. Carlitz, L. Generating Functions. The Fibonacci Quarterly. 7 (1969): 359-393.
  10. Carlitz, L. Enumeration of Sequences by Rises and Falls: A Refinement of the Simon Newcomb Problem. Duke Mathematical Journal. 39 (1972): 267-280.
  11. Carlitz, L., J. Riordan. Two Element Lattice Permutation Numbers and Their q-generalization. Duke Mathematical Journal. 31 (1964): 271-388.
  12. Riordan, J. A Note on a q-extension of Ballot Numbers. Journal of Combinatorial Theory. 4 (1968): 191-193.
  13. Shannon. A.G. Some q-Binomial Coefficients Formed from Rising Factorials. Notes on Number Theory and Discrete Mathematics. 12 (2006): 13-20.

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Cite this paper

APA

Shannon A. G. (2008). Cycles of binomial coefficients. Notes on Number Theory and Discrete Mathematics, 14(3), 19-24.

Chicago

Shannon, AG. “Cycles of Binomial Coefficients.” Notes on Number Theory and Discrete Mathematics 14, no. 3 (2008): 19-24.

MLA

Shannon, AG. “Cycles of Binomial Coefficients.” Notes on Number Theory and Discrete Mathematics 14.3 (2008): 19-24. Print.

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