Log-concavity of the partition function

被引：80

作者：

DeSalvo, Stephen ^{[1
]}

Pak, Igor ^{[1
]}

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

来源：

RAMANUJAN JOURNAL | 2015年 / 38卷 / 01期

关键词：

Integer partition; Partition function; Log-concave sequence; Asymptotic analysis; Error estimates; ASYMPTOTIC FORMULAS; COMBINATORIAL PROOF; UNIMODAL SEQUENCES; SERIES; NUMBERS; STACKS;

D O I：

10.1007/s11139-014-9599-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the partition function is log-concave for all . We then extend the results to resolve two related conjectures by Chen and one by Sun. The proofs are based on Lehmer's estimates on the remainders of the Hardy-Ramanujan and the Rademacher series for p(n).

引用

页码：61 / 73

页数：13

共 25 条

[1] COMBINATORIAL PROOF OF A PARTITION FUNCTION LIMIT [J].

ANDREWS, GE .

AMERICAN MATHEMATICAL MONTHLY, 1971, 78 (03) :276-&

[2]

[Anonymous], 2010, FPSAC 2010 C TALK SL

[3]

[Anonymous], 1998, CAMBRIDGE MATH LIB

[4]

Bessenrodt C., Maximal multiplicative properties of partitions

[5]

Bona M., 2004, ELECTRON J COMB, V11, P4

[6]

Brenti F., 1994, Contemporary Mathematics, V178, P71

[7] Asymptotic formulas for stacks and unimodal sequences [J].

Bringmann, Kathrin ;

Mahlburg, Karl .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2014, 126 :194-215

[8]

Chen W.Y.C., 2014, ARXIV14070177

[9] On an elementary proof of some asymptotic formulas in the theory of partitions [J].

Erdos, P .

ANNALS OF MATHEMATICS, 1942, 43 :437-450

[10]

Gupta H., 1939, TABLES PARTITIONS

← 1 2 3 →