We derive an asymptotic formula for p n (N,M), the number of partitions of integer n with part size at most N and length at most M. We consider both N and M are comparable to n. This is an extension of the classical Hardy-Ramanujan formula and Szekeres' formula. The proof relies on the saddle point method.
|Original language||English (US)|
|Number of pages||32|
|Journal||Journal of Number Theory|
|State||Published - Aug 2019|
Bibliographical noteFunding Information:
The research of Tiefeng Jiang is supported in part by NSF Grant DMS-1209166 and DMS-1406279.Ke Wang is supported by HKUST Initiation Grant IGN16SC05.
© 2019 Elsevier Inc.
- Asymptotic formula
- Restricted integer partitions