{"title":"Equalities for the 𝑟3-Crank of 3-Regular Overpartitions","authors":"Robert X. J. Hao, Erin Y. Y. Shen","doi":"10.1556/012.2023.01542","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"22 6","pages":"0"},"PeriodicalIF":0.4000,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Scientiarum Mathematicarum Hungarica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1556/012.2023.01542","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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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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.
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