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.
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页码：1521 / 1543
页数：23
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