3-正则过分区𝑟3-Crank的等式

IF 0.4 4区数学 Q4 MATHEMATICS

Studia Scientiarum Mathematicarum Hungarica 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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来源期刊

Studia Scientiarum Mathematicarum Hungarica 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research papers on various fields of mathematics, e.g., algebra, algebraic geometry, analysis, combinatorics, dynamical systems, geometry, mathematical logic, mathematical statistics, number theory, probability theory, set theory, statistical physics and topology.