Linear inequalities concerning the sum of the distinct parts congruent to r modulo m in all the partitions of n

被引：1

作者：

Merca, Mircea ^{[1
]}

机构：

[1] Univ Politehn Bucuresti, Fundamental Sci Appl Engn Res Ctr, Dept Math Methods & Models, RO-060042 Bucharest, Romania

来源：

QUAESTIONES MATHEMATICAE | 2023年 / 46卷 / 12期

关键词：

Integer partitions; partition identities; partition inequalities; truncated theta; IDENTITIES;

D O I：

10.2989/16073606.2023.2174911

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the sum of the parts congruent to r modulo m counted without multiplicity in all the partitions of n. Considering truncated theta series, we introduce a collection of infinite families of linear inequalities involving this sum. We provide connections with partitions with nonnegative rank, partition with non- negative crank and Garden of Eden partitions.

引用

页码：2637 / 2659

页数：23

共 20 条

[1]

Andrews G.E., 1976, The Theory of Partitions

[2] DYSONS CRANK OF A PARTITION [J].