Refinements of Equalities and Inequalities on d-Cranks for Partitions with Designated Summands

被引：0
|
作者：
Robert X. J. Hao
Y. Zhang
机构：
[1] Nanjing Institute of Technology,College of Science and Mathematics
来源：
Bulletin of the Malaysian Mathematical Sciences Society | 2022年 / 45卷
关键词：
Partition statistic; Crank; Combinatorial interpretation; Refinement; 05A17; 11P83;
D O I：
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学科分类号：
摘要：
Andrews, Lewis, and Lovejoy introduced partitions with designated summands. Let PD(n) enumerate partitions with designated summands of n. Andrews et al. gave a Ramanujan-type congruence mod 3 satisfied by PD(n). Recently, Shen defined the d-crank on partitions with designated summands to provide a combinatorial interpretation for this congruence. Shen also derived some equalities and inequalities on d-cranks. In this paper, we refine some equalities and inequalities given by Shen. Meanwhile, we establish a refinement of the Ramanujan-type congruence of Andrews et al.
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页码：1987 / 2002
页数：15
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