On a problem on restricted k-colored partitions, II

被引:1
作者
Ma, Wu-Xia [1 ]
Chen, Yong-Gao [2 ,3 ]
机构
[1] Nanjing Univ Posts & Telecommun, Coll Sci, Nanjing 210023, Peoples R China
[2] Nanjing Normal Univ, Sch Math Sci, Nanjing 210023, Peoples R China
[3] Nanjing Normal Univ, Inst Math, Nanjing 210023, Peoples R China
基金
中国国家自然科学基金;
关键词
Partitions; Colored partitions; Congruence; Arithmetic progression; Dirichlet's theorem; CONGRUENCES MODULO POWERS; OVERPARTITIONS;
D O I
10.1007/s11139-023-00806-1
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
For two integers 1 <= j <= k, we define (k, j)-colored partitions to be those partitions in which parts may appear in k different types and at most j types can appear for a given part size. Let c(k,j)(n) be the number of (k, j)-colored partitions of n. Recently, Keith studied (k, j)-colored partitions and proved the following results: For j is an element of {2,5,8,9}, we have c(9,j )(3n+2) equivalent to 0 (mod 27) for all n >= 0. For j is an element of {3,6}, we have c(9,j )(9n+2) equivalent to 0 (mod 27) for all n >= 0. In this paper, we determine all a, b, c, j with (a,b)=1 and 1 <= j <= 8 such that c(9,j )(an + b) equivalent to c (mod27) for all nonnegative integers n.
引用
收藏
页码:1109 / 1118
页数:10
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