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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## Details

### 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

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- Carlitz, L. Enumeration of Sequences by Rises and Falls: A Refinement of the Simon Newcomb Problem. Duke Mathematical Journal. 39 (1972): 267-280.
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- Shannon. A.G. Some q-Binomial Coefficients Formed from Rising Factorials. Notes on Number Theory and Discrete Mathematics. 12 (2006): 13-20.

## Related papers

## Cite this paper

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

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

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