{"title":"Pattern avoidance in partial words over a ternary alphabet","authors":"Adam Gagol","doi":"10.1515/UMCSMATH-2015-0013","DOIUrl":null,"url":null,"abstract":"Blanched-Sadri and Woodhouse in 2013 have proven the conjecture of Cassaigne, stating that any pattern with \\(m\\) distinct variables and of length at least \\(2^m\\) is avoidable over a ternary alphabet and if the length is at least \\(3\\cdot 2^{m-1}\\) it is avoidable over a binary alphabet. They conjectured that similar theorems are true for partial words – sequences, in which some characters are left “blank”. Using method of entropy compression, we obtain the partial words version of the theorem for ternary words.","PeriodicalId":340819,"journal":{"name":"Annales Umcs, Mathematica","volume":"52 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Umcs, Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/UMCSMATH-2015-0013","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
Blanched-Sadri and Woodhouse in 2013 have proven the conjecture of Cassaigne, stating that any pattern with \(m\) distinct variables and of length at least \(2^m\) is avoidable over a ternary alphabet and if the length is at least \(3\cdot 2^{m-1}\) it is avoidable over a binary alphabet. They conjectured that similar theorems are true for partial words – sequences, in which some characters are left “blank”. Using method of entropy compression, we obtain the partial words version of the theorem for ternary words.