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)

Research output: Contribution to journal › Article › peer-review

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

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Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

Asymptotic formula
Restricted integer partitions

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10.1016/j.jnt.2019.02.006

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title = "A generalized Hardy-Ramanujan formula for the number of restricted integer partitions",

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.",

keywords = "Asymptotic formula, Restricted integer partitions",

author = "Tiefeng Jiang and Ke Wang",

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year = "2019",

month = aug,

doi = "10.1016/j.jnt.2019.02.006",

language = "English (US)",

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AU - Jiang, Tiefeng

AU - Wang, Ke

PY - 2019/8

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N2 - 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.

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.

KW - Asymptotic formula

KW - Restricted integer partitions

UR - https://www.scopus.com/pages/publications/85063497005

UR - https://www.scopus.com/pages/publications/85063497005#tab=citedBy

U2 - 10.1016/j.jnt.2019.02.006

DO - 10.1016/j.jnt.2019.02.006

M3 - Article

AN - SCOPUS:85063497005

SN - 0022-314X

VL - 201

SP - 322

EP - 353

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

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

Abstract

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Keywords

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