一类约束分拆函数的同余性质

Congruence Properties of a Class of Restricted Overpartition Functions

摘要: 利用q级数中的dissection公式及Radu算法，研究了一类特殊的overpartition函数${\overline{t}}^{\left(k\right)}\left(n\right)$ 的同余性质，得到了$\overline{t}\left(n\right)$ 模3及${\overline{t}}^{\left(3\right)}\left(n\right)$ 模2、模4、模8的同余式。此外，得到了${\overline{t}}^{\left(8\right)}\left(n\right)$ 模3时与五角数的同余关系。

Abstract: Using the dissection formula in q-series and Radu’s algorithm, we investigate the congruence properties of a class of special overpartition functions ${\overline{t}}^{\left(k\right)}\left(n\right)$ . We obtain congruences modulo 3 for $\overline{t}\left(n\right)$ ，and modulo 2, 4 and 8 for ${\overline{t}}^{\left(3\right)}\left(n\right)$ . Moreover, we establish a congruence relation for ${\overline{t}}^{\left(8\right)}\left(n\right)$ modulo 3 involving pentagonal numbers.