Arithmetic properties of l-regular overpartitions

作者：Shen, Erin Y. Y.^*

来源：International Journal of Number Theory, 2016, 12(3): 841-852.

DOI：10.1142/S1793042116500548

• Congruence
• rank
• overpartition
• regular partition

Recently, Andrews introduced the partition C) over bar (k,i)(n) as the number of overpartitions of n in which no part is divisible by k and only parts equivalent to +/- i (mod k) may be overlined. He proved that (C) over bar (3,1)(9n + 3) and (C) over bar (3,1)(9n + 6) are divisible by 3. Let (A) over bar (l)(n) be the number of overpartitions of n into parts not divisible by l. In this paper, we call the overpartitions enumerated by the A) over bar (l)(n) l-regular overpartitions. For (A) over bar (3)(n) and (A) over bar (4)(n), we obtain some explicit results on the generating function dissections. We also derive some congruences for (A) over bar (l)(n) modulo 3, 6 and 24 which imply the congruences for (C) over bar (3,1)(n) proved by Andrews.

• 出版日期2016-5
• 单位河海大学