Rank and congruences for overpartition pairs

被引：41

作者：

Bringmann, Kathrin ^{[1
]}

Lovejoy, Jeremy ^{[2
]}

机构：

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[2] Univ Paris 07, CNRS, LIAFA, F-75251 Paris 05, France

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2008年 / 4卷 / 02期

关键词：

partitions; overpartitions; overpartition pairs; congruences; Dyson's rank; modular forms;

D O I：

10.1142/S1793042108001353

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The rank of an overpartition pair is a generalization of Dyson's rank of a partition. The purpose of this paper is to investigate the role that this statistic plays in the congruence properties of (pp) over bar (n), the number of overpartition pairs of n. Some generating functions and identities involving this rank are also presented.

引用

页码：303 / 322

页数：20

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