Khaled Ben Letaïef

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 23, 2017, Number 3, Pages 27—34

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## Details

### Authors and affiliations

Khaled Ben Letaïef

*Aeronautics and aerospace high graduate engineer
16 Bd du Maréchal de Lattre, apt. 095, 21300 Chenove, France
*

### Abstract

Associated Stirling numbers of first and second kind are usually found in the literature in various forms of stairs depending on their order *r*. Yet, it is shown in this note that all of these numbers can be arranged, through a linear transformation, in the same arithmetical triangle structure as the “Pascal’s triangle”.

### Keywords

- Number theory
- Associated Stirling numbers
- Arithmetical triangle

### AMS Classification

- 11B73
- 05A18

### References

- Comtet, L. (1970) Analyse combinatoire, PUF.
- Hilton, P. & Pedersen, J. (1999) Two recurrence relations for Stirling factors, Bulletin Belg. Math. Soc. Simon Stevin, 6, 615–623.
- Hilton, P., et al. (1994) On partitions, surjections and Stirling numbers, Bulletin Belg. Math. Soc. Simon Stevin, 1, 713–725.
- Howard, F.T. (1990), Congruences for the Stirling numbers and associated Stirling numbers, Acta Arithmetica, LV, 29–41.
- Sandor, J., & Crstici, B. (2004) Handbook of number theory II, Kluwer Acad. Publ., Chapter 5, 459–618.
- Weisstein, Eric W., “Stirling Number of the Second Kind.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html
- Weisstein, Eric W., “Stirling Number of the First Kind.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/StirlingNumberoftheFirstKind.html
- Weisstein, Eric W., “Permutation Cycle.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/PermutationCycle.html

## Related papers

## Cite this paper

APALetaïef, K. B. (2017). All associated Stirling numbers are arithmetical triangles. Notes on Number Theory and Discrete Mathematics, 23(2), 27-34.

ChicagoLetaïef, Khaled Ben. “All associated Stirling numbers are arithmetical triangles.” Notes on Number Theory and Discrete Mathematics 23, no. 2 (2017): 27-34.

MLALetaïef, Khaled Ben. “All associated Stirling numbers are arithmetical triangles.” Notes on Number Theory and Discrete Mathematics 23.2 (2017): 27-34. Print.