On partitions without small parts
Journal de théorie des nombres de Bordeaux, Volume 12 (2000) no. 1, p. 227-254

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, and 1mc 1 n logn c 2 .

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, et 1mc 1 n logn c 2 .

@article{JTNB_2000__12_1_227_0,
     author = {Nicolas, Jean-Louis and S\'ark\"ozy, Andr\'as},
     title = {On partitions without small parts},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {12},
     number = {1},
     year = {2000},
     pages = {227-254},
     zbl = {1005.11049},
     mrnumber = {1827850},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2000__12_1_227_0}
}
Nicolas, J.-L.; Sárközy, A. On partitions without small parts. Journal de théorie des nombres de Bordeaux, Volume 12 (2000) no. 1, pp. 227-254. http://www.numdam.org/item/JTNB_2000__12_1_227_0/

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