Arithmetic properties for Andrews’ (48,6)- and (48,18)-singular overpartitions
Arithmetic properties for Andrews’ (48,6)- and (48,18)-singular overpartitions
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DOI：
10.1515/math-2019-0026
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发表时间：
2019-01
期刊：
影响因子：
1.7
通讯作者：
Eric H. Liu;Wenjing Du
中科院分区：
文献类型：
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作者：
Eric H. Liu;Wenjing Du
奇异超配分函数是由Andrews定义的。令Ck，i（n）表示n的（k，i）-奇异超划分的个数，它计算n的没有部分可被k整除且只有±i（mod k）部分可被覆盖的超划分的个数。Ahmed和Baruah，Andrews，Chen，赫什霍恩和Sellers，Naika和Gireesh，Shen和Yao等对（k，i）发现了Ck，i（n）的模3，9同余和模2幂同余。本文证明了C48，6（n）和C48，18（n）的模2幂同余。
Abstract Singular overpartition functions were defined by Andrews. Let Ck,i(n) denote the number of (k, i)-singular overpartitions of n, which counts the number of overpartitions of n in which no part is divisible by k and only parts ±i (mod k) may be overlined. A number of congruences modulo 3, 9 and congruences modulo powers of 2 for Ck,i(n) were discovered by Ahmed and Baruah, Andrews, Chen, Hirschhorn and Sellers, Naika and Gireesh, Shen and Yao for some pairs (k, i). In this paper, we prove some congruences modulo powers of 2 for C48, 6(n) and C48, 18(n).