Mladen Vassilev-Missana and Krassimir Atanassov

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 14, 2008, Number 2, Pages 11—14

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Mladen Vassilev-Missana

Krassimir Atanassov

### Abstract

In the paper the maximal elements of the set {*D(n − k*, *k* | *k* = 0, 1, …, *n*} are found, where *D*(*p*, *q*) are the so-called Delannoy numbers and *n* ≥ 2 is a natural number. It is shown that for an even n the number D(*n*/2, *n*/2) is the maximal element of the mentioned set, while when n is odd – the maximal elements are two D([*n*/2]+1, [*n*/2]) and D([*n*/2], [*n*/2]+1).

### References

- Comtet, L. Advanced Combinatorics, D. Reidel Publ. Co. Dordrecht, 1974.
- Vassilev M., Atanassov K., On Delanoy numbers, Annuaire de l’Universite de Sofia “St. Kliment Ohridski”, Faculte de Mathematiques et Informatique, Livre 1 – Mathematiques, Tome 81, 1987, 153-162.

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## Cite this paper

APAVassilev-Missana, M. & Atanassov, K. (2008). On an extremal problem related to the Delannoy numbers. Notes on Number Theory and Discrete Mathematics, 14(2), 11-14.

ChicagoVassilev-Missana, M, and K Atanassov. “On an Extremal Problem Related to the Delannoy Numbers.” Notes on Number Theory and Discrete Mathematics 14, no. 2 (2008): 11-14.

MLAVassilev-Missana, M, and K Atanassov. “On an Extremal Problem Related to the Delannoy Numbers.” Notes on Number Theory and Discrete Mathematics 14.2 (2008): 11-14. Print.