3-正则过分区𝑟3-Crank的等式

Pub Date : 2023-10-24 DOI:10.1556/012.2023.01542

Robert X. J. Hao, Erin Y. Y. Shen

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引用次数: 0

摘要

Lovejoy引入了分区函数，表示𝑛的𝑙-regular过度分区的数量。Andrews定义了用配分函数计数的(𝑘，)-奇异过划分，并指出。同时，Andrews导出了一个有趣的可除性(mod 3)。最近，我们构造了𝑙-regular overpartitions的划分统计量𝑟𝑙-曲柄，并对Andrews的一些同余和Andrews的一些同余给出了组合解释。在本文中，我们旨在证明3正则过分割的𝑟3-曲柄的一些等式。

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Equalities for the 𝑟3-Crank of 3-Regular Overpartitions

Lovejoy introduced the partition function as the number of 𝑙-regular overpartitions of 𝑛. Andrews defined (𝑘, 𝑖)-singular overpartitions counted by the partition function , and pointed out that . Meanwhile, Andrews derived an interesting divisibility property that (mod 3). Recently, we constructed the partition statistic 𝑟 𝑙 -crank of 𝑙-regular overpartitions and give combinatorial interpretations for some congruences of as well as the congruences of Andrews. In this paper, we aim to prove some equalities for the 𝑟 3 -crank of 3-regular overpartitions.

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