A generalized Hardy-Ramanujan formula for the number of restricted integer partitions

Tiefeng Jiang; Ke Wang

doi:10.1016/j.jnt.2019.02.006

A generalized Hardy-Ramanujan formula for the number of restricted integer partitions

Tiefeng Jiang, Ke Wang

Statistics (Twin Cities)

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3 Scopus citations

Abstract

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)
Pages (from-to)	322-353
Number of pages	32
Journal	Journal of Number Theory
Volume	201
DOIs	https://doi.org/10.1016/j.jnt.2019.02.006
State	Published - Aug 2019

Bibliographical note

Funding 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.

Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

Asymptotic formula
Restricted integer partitions

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AB - 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.

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ER -

A generalized Hardy-Ramanujan formula for the number of restricted integer partitions

Abstract

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Keywords

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