Congruences modulo powers of 3 for 3-and 9-colored generalized Frobenius partitions

被引：5
|
作者：
Wang, Liuquan [1 ]
机构：
[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China
来源：
DISCRETE MATHEMATICS | 2018年 / 341卷 / 12期
基金：
中国国家自然科学基金;
关键词：
Congruences; Generalized Frobenius partitions; Modulo powers of 3; 6; COLORS; RAMANUJAN; ANDREWS;
D O I：
10.1016/j.disc.2018.08.024
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let c phi(k)(n) be the number of k-colored generalized Frobenius partitions of n. We establish some infinite families of congruences for c phi(3)(n) and c phi(9) (n) modulo arbitrary powers of 3, which refine the results of Kolitsch. For example, for k >= 3 and n >= 0, we prove that c phi(3)(3(2k)n + 7 . 3(2k) + 1/8) 0 (mod 3(4k+5)). We give two different proofs to the congruences satisfied by c phi(9)(n). One of the proofs uses a relation between c phi(9)(n) and c phi(3)(n) due to Kolitsch, for which we provide a new proof in this paper. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：3370 / 3384
页数：15
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