On partitions without small parts

J.-L. Nicolas; A. Sárközy

J.-L. Nicolas ; A. Sárközy

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

Résumé
Abstract

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 $1 \leq m \leq c_{1} \frac{n}{{(log n)}^{c_{2}}}$ .

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 $1 \leq m \leq c_{1} \frac{n}{{(log n)}^{c_{2}}}$ .

MR Zbl

@article{JTNB_2000__12_1_227_0,
     author = {J.-L. Nicolas and A. S\'ark\"ozy},
     title = {On partitions without small parts},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {227--254},
     publisher = {Universit\'e Bordeaux I},
     volume = {12},
     number = {1},
     year = {2000},
     zbl = {1005.11049},
     mrnumber = {1827850},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_2000__12_1_227_0/}
}

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J.-L. Nicolas; A. Sárközy. On partitions without small parts. Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 1, pp. 227-254. https://jtnb.centre-mersenne.org/item/JTNB_2000__12_1_227_0/

Bibliographie
Cité par

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