Journal of Integer Sequences, Vol. 10 (2007), Article 07.6.3

Integer Partitions and Convexity

Sadek Bouroubi
Faculty of Mathematics
Department of Operational Research
Laboratory LAID3
P. O. Box 32
16111 El-Alia
Bab-Ezzouar, Algiers


Let n be an integer >=1, and let p(n,k) and P(n,k) count the number of partitions of n into k parts, and the number of partitions of n into parts less than or equal to k, respectively. In this paper, we show that these functions are convex. The result includes the actual value of the constant of Bateman and Erdős.

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(Concerned with sequence A026812.)

Received March 6 2007; revised version received June 9 2007. Published in Journal of Integer Sequences, June 10 2007.

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