{"title":"Bounds on the size of Progression-Free Sets in ℤ<i>\n <sub>m</sub>\n <sup>n</sup>\n </i>","authors":"P. Pach","doi":"10.2478/udt-2022-0005","DOIUrl":null,"url":null,"abstract":"\n In this note we give an overview of the currently known best lower and upper bounds on the size of a subset of ℤ\n n\n m\n avoiding k-term arithmetic progression. We will focus on the case when the length of the forbidden progression is 3. We also formulate some open questions.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Uniform distribution theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/udt-2022-0005","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
In this note we give an overview of the currently known best lower and upper bounds on the size of a subset of ℤ
n
m
avoiding k-term arithmetic progression. We will focus on the case when the length of the forbidden progression is 3. We also formulate some open questions.
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