{"title":"Pattern avoidance and dominating compositions","authors":"Krishna Menon, Anurag Singh","doi":"10.54550/eca2022v2s1r4","DOIUrl":null,"url":null,"abstract":"Jel\\'inek, Mansour, and Shattuck studied Wilf-equivalence among pairs of patterns of the form $\\{\\sigma,\\tau\\}$ where $\\sigma$ is a set partition of size $3$ with at least two blocks. They obtained an upper bound for the number of Wilf-equivalence classes for such pairs. We show that their upper bound is the exact number of equivalence classes, thus solving a problem posed by them.","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"40 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Enumerative Combinatorics and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.54550/eca2022v2s1r4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Jel\'inek, Mansour, and Shattuck studied Wilf-equivalence among pairs of patterns of the form $\{\sigma,\tau\}$ where $\sigma$ is a set partition of size $3$ with at least two blocks. They obtained an upper bound for the number of Wilf-equivalence classes for such pairs. We show that their upper bound is the exact number of equivalence classes, thus solving a problem posed by them.