On some infinite families of congruences for [j, k]-partitions into even parts distinct

被引：0

作者：

Naika, M. S. Mahadeva ^{[1
]}

Harishkumar, T. ^{[2
]}

Veeranayaka, T. N. ^{[2
]}

机构：

[1] Bengaluru City Univ, Dept Math, Cent Coll Campus, Bengaluru 560001, Karnataka, India

[2] Bangalore Univ, Dept Math, Cent Coll Campus, Bengaluru 560001, Karnataka, India

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2021年 / 52卷 / 04期

关键词：

Congruences; Partitions with even parts distinct; j k]-partitions; ARITHMETIC PROPERTIES; PARTITIONS; BIPARTITIONS; NUMBER;

D O I：

10.1007/s13226-021-00046-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we define the partition function ped(j,k)(n), the number of [j, k]-partitions of n into even parts distinct, where none of the parts are congruent to j (mod k) (where k > j >= 1). We obtain many infinite families of congruences modulo powers of 2 for ped(3,6)(n) and congruences modulo powers of 2 and 3 for ped(9,18)(n). For example, for all n >= 0 and alpha, beta >= 0, ped(9),(18) (2 . 3(4 alpha+4) . 7(2 beta+1) (7n + s) + 11 . 3(4 alpha+3) . 7(2 beta+1) + 1/4) equivalent to 0 (mod 16), where s = 0, 2, 3, 4, 5, 6.

引用

页码：1038 / 1054

页数：17