Geodesic
Integer partitions and convexity
Journal of integer sequences, Tome 10 (2007) no. 6
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.
Classification : 11P81
Keywords: integer partition, convexity 
@article{JIS_2007__10_6_a5,
     author = {Bouroubi,  Sadek},
     title = {Integer partitions and convexity},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {6},
     zbl = {1140.11345},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_6_a5/}
}
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Bouroubi,  Sadek. Integer partitions and convexity. Journal of integer sequences, Tome 10 (2007) no. 6. http://geodesic.mathdoc.fr/item/JIS_2007__10_6_a5/