On partitions without small parts

Nicolas, J.-L.; Sárközy, A.

Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 1, pp. 227-254.

On désigne par $r(n,m)$ le nombre de partitions de l’entier $n$ en parts supérieures ou égales à $m$. En appliquant la méthode du point selle à la série génératrice, nous donnons une estimation asymptotique de $r(n,m)$ valable pour $n\to \infty$, et $1\le m\le c_1{\displaystyle \frac{n}{{\left(logn\right)}^{c_2}}}$.

Let $r(n,m)$ denote the number of partitions of $n$ into parts, each of which is at least $m$. By applying the saddle point method to the generating series, an asymptotic estimate is given for $r(n,m)$, which holds for $n\to \infty$, and $1\le m\le c_1{\displaystyle \frac{n}{{\left(logn\right)}^{c_2}}}$.

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