Arithmetic Properties of 5-Tuple Partitions with 3-Cores

被引：0

作者：

Wen, Xin-Qi ^{[1
]}

机构：

[1] Tianjin Univ, Sch Math, Tianjin 300350, Peoples R China

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2022年 / 45卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Partition; Congruence; k-tuple; t-core; Ramanujan's theta function; INFINITE FAMILIES; BIPARTITIONS; CONGRUENCES; IDENTITIES; TRIPLES; ANALOGS;

D O I：

10.1007/s40840-022-01282-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A(3,5)(n) denote the number of 5-tuple partitions of n with 3-cores. We establish some congruences modulo 2, 4, 5, 8 and 10 for A3,5(n) by employing q-series identities. For example, we prove for any prime p >= 5, alpha >= 1, beta >= 0 and n >= 0, A(3,5) (2(2 alpha+2)p(2 beta+2)n + (6 j + p) . 2(2 alpha+1) p2(beta+1) - 5/3) equivalent to 0 (mod 2), where 1 <= j <= p - 1.

引用

页码：1521 / 1543

页数：23

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