Partitions associated with the Ramanujan/Watson mock theta functions ω(q), ν(q)and ϕ(q)
Partitions associated with the Ramanujan/Watson mock theta functions ω(q), ν(q)and ϕ(q)
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DOI：
10.1007/s40993-015-0020-8
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发表时间：
2015-12
影响因子：
0.8
通讯作者：
G. Andrews;A. Dixit;A. Yee
中科院分区：
文献类型：
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作者：
G. Andrews;A. Dixit;A. Yee
分区的生成函数具有重复的（resp）。不同的)部分，使得每个奇数部分小于两倍最小的部分显示为三阶模拟函数ω(q) （respo .ν(−q)）。对每个偶部具有相应限制的分区也得到了类似的结果，其中一个涉及三阶模拟θ函数φ (q)。得到了与这些划分相关联的最小部分配分函数的同余。本文还得到了欧拉五边形数定理的分划理论解释的两个类似的例子。
The generating function of partitions with repeated (resp. distinct) parts such that each odd part is less than twice the smallest part is shown to be the third order mock theta functionω(q) (resp.ν(−q)). Similar results for partitions with the corresponding restriction on each even part are also obtained, one of which involves the third order mock theta functionϕ(q). Congruences for the smallest parts partition function(s) associated to such partitions are obtained. Two analogues of the partition-theoretic interpretation of Euler’s pentagonal number theorem are also obtained.