{"title":"列举带有禁止因子的单词","authors":"Richard Pinch","doi":"10.1016/j.endm.2019.02.003","DOIUrl":null,"url":null,"abstract":"<div><p>This presentation is an exposition of an application of the theory of recurrence relations to enumerating strings over an alphabet with a forbidden factor (consecutive substring). As an illustration we examine the case of binary strings with a forbidden factor of k consecutive symbols <strong>1</strong> for given k, using generating function techniques that deserve to be better known.</p><p>This allows us to derive a known upper bound for the number of prefix normal binary words: words with the property that no factor has more occurrences of the symbol <strong>1</strong> than the prefix of the same length. Such words arise in the context of indexed binary jumbled pattern matching.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2019.02.003","citationCount":"0","resultStr":"{\"title\":\"Enumerating words with forbidden factors\",\"authors\":\"Richard Pinch\",\"doi\":\"10.1016/j.endm.2019.02.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This presentation is an exposition of an application of the theory of recurrence relations to enumerating strings over an alphabet with a forbidden factor (consecutive substring). As an illustration we examine the case of binary strings with a forbidden factor of k consecutive symbols <strong>1</strong> for given k, using generating function techniques that deserve to be better known.</p><p>This allows us to derive a known upper bound for the number of prefix normal binary words: words with the property that no factor has more occurrences of the symbol <strong>1</strong> than the prefix of the same length. Such words arise in the context of indexed binary jumbled pattern matching.</p></div>\",\"PeriodicalId\":35408,\"journal\":{\"name\":\"Electronic Notes in Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.endm.2019.02.003\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Notes in Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1571065319300034\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Notes in Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1571065319300034","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
This presentation is an exposition of an application of the theory of recurrence relations to enumerating strings over an alphabet with a forbidden factor (consecutive substring). As an illustration we examine the case of binary strings with a forbidden factor of k consecutive symbols 1 for given k, using generating function techniques that deserve to be better known.
This allows us to derive a known upper bound for the number of prefix normal binary words: words with the property that no factor has more occurrences of the symbol 1 than the prefix of the same length. Such words arise in the context of indexed binary jumbled pattern matching.
期刊介绍：
Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.
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