Avoiding and Enforcing Repetitive Structures in Words

Avoiding and Enforcing Repetitive Structures in Words
Author :
Publisher : BoD – Books on Demand
Total Pages : 174
Release :
ISBN-10 : 9783734741975
ISBN-13 : 3734741971
Rating : 4/5 (971 Downloads)

Book Synopsis Avoiding and Enforcing Repetitive Structures in Words by : Mike Müller

Download or read book Avoiding and Enforcing Repetitive Structures in Words written by Mike Müller and published by BoD – Books on Demand. This book was released on 2014-12-15 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Avoiding and enforcing repetitions in words are central topics in the area of combinatorics on words, with first results going back to the beginning of the 20th century. The results presented in this thesis extend and enrich the existing theory concerning the presence and absence of repetitive structures in words. In the first part the question whether such structures necessarily appear in infinite words over a finite alphabet is investigated. In particular, avoidability questions of patterns whose repetitive structure is disguised by the application of a permutation are studied. The second part deals with equations on words that enforce a certain repetitive structure involving involutions in their solution set. A generalisation of the classical equations u^l = v^mw^n that were studied by Lyndon and Schützenberger is analysed. The last part considers the influence of the shuffle operation on square-free words and related avoidability questions.


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