A general asymptotic formula for distinct partitions

被引：0

作者：

Brunel, Vivien ^{[1
]}

机构：

[1] Leonard de Vinci Pole Univ, Finance Lab, Courbevoie, France

来源：

ANNALS OF PHYSICS | 2018年 / 394卷

关键词：

Integer partitions; Analytic combinatorics; Distinct partitions; Asymptotics; Saddle-point; INTEGER-PARTITIONS; NUMBER;

D O I：

10.1016/j.aop.2018.03.023

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Many asymptotic formulas exist for unrestricted integer partitions as well as for equal partitions of integers into a finite number of parts. We use an analogy with fermion gases and the tools of statistical physics to derive asymptotic formulas for distinct partitions with a large but finite number of parts. These results are supported by the fact that we recover some other existing asymptotic results and by numerical comparisons with exact results. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：73 / 83

页数：11

共 50 条

[21] A formula for the number of partitions of n in terms of the partial Bell polynomials [J].

Jha, Sumit Kumar .

RAMANUJAN JOURNAL, 2022, 57 (02) :845-848

[22] Asymptotic formulas related to the M2-rank of partitions without repeated odd parts [J].

Jennings-Shaffer, Chris ;

Reihill, Dillon .

RAMANUJAN JOURNAL, 2020, 52 (01) :175-242

[23] INEQUALITIES AND UNIFORM ASYMPTOTIC FORMULAE FOR SPT-CRANK OF PARTITIONS [J].

Chen, Yuan ;

Zhou, Nian Hong .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2025, 111 (01) :56-67

[24] On the number of partitions of a number into distinct divisors [J].

Lebowitz-Lockard, Noah ;

Vandehey, Joseph .

NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2024, 30 (03) :654-661

[25] On the partitions into distinct parts and odd parts [J].

Merca, Mircea .

QUAESTIONES MATHEMATICAE, 2021, 44 (08) :1095-1105

[26] On the asymptotic distribution of cranks and ranks of cubic partitions [J].

Kim, Byungchan ;

Kim, Eunmi ;

Nam, Hayan .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 443 (02) :1095-1109

[27] Asymptotic behavior of Odd-Even partitions [J].

Jang, Min-Joo .

ELECTRONIC JOURNAL OF COMBINATORICS, 2017, 24 (03)

[28] UNIFORM ASYMPTOTIC FORMULAS FOR RESTRICTED BIPARTITE PARTITIONS [J].

Zhou, Nian Hong .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2020, 102 (02) :217-225

[29] Enumeration and Asymptotic Formulas for Rectangular Partitions of the Hypercube [J].

Au, Yu Hin ;

Bagherzadeh, Fatemeh ;

Bremner, Murray R. .

JOURNAL OF INTEGER SEQUENCES, 2020, 23 (01)

[30] Congruences for the number of k-tuple partitions with distinct even parts [J].

Chen, Shi-Chao .

DISCRETE MATHEMATICS, 2013, 313 (15) :1565-1568

← 1 2 3 4 5 →