Congruences modulo 9 and 27 for overpartitions
Congruences modulo 9 and 27 for overpartitions
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DOI：
10.1007/s11139-015-9739-z
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发表时间：
2015-12
期刊：
影响因子：
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通讯作者：
Ernest X. W. Xia
中科院分区：
文献类型：
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作者：
Ernest X. W. Xia
记n的超划分数。Fortin等.和赫什霍恩和塞勒斯建立了一些同余模2的权力。最近，Xia和Yao发现了几个模2和3的幂的同余。特别是，他们证明了这一点。本文推广了这两个同余式，建立了模9和模27的几个新的无穷同余族。利用库珀等人的一些结果，证明了模9和模27的一些奇异同余，例如，证明了模9和模27的奇异同余.我们也给出了关于的同余的两个定理。
Letdenote the number of overpartitions ofn. Fortin et al. and Hirschhorn and Sellers established some congruences modulo powers of 2 for. Recently, Xia and Yao found several congruences modulo powers of 2 and 3. In particular, they proved thatand. In this paper, we generalize the two congruences and establish several new infinite families of congruences modulo 9 and 27 for. Furthermore, we prove some strange congruences modulo 9 and 27 forby employing some results due to Cooper et al. For example, we prove that for,and. We also present two conjectures on congruences for.