On Sturmian and Episturmian words, and related topics
| dc.contributor.advisor | Wolff, Alison | en |
| dc.contributor.advisor | Clarke, Robert John | en |
| dc.contributor.author | Glen, Amy Louise | en |
| dc.contributor.school | School of Mathematical Sciences | en |
| dc.date.issued | 2006 | en |
| dc.description.abstract | In recent years, combinatorial properties of finite and infinite words have become increasingly important in fields of physics, biology, mathematics, and computer science. In particular, the fascinating family of Sturmian words has become an extremely active subject of research. These infinite binary sequences have numerous applications in various fields of mathematics, such as symbolic dynamics, the study of continued fraction expansion, and also in some domains of physics ( quasicrystal modelling ) and computer science ( pattern recognition, digital straightness ). There has also been a recent surge of interest in a natural generalization of Sturmian words to more than two letters - the so - called episturmian words, which include the well - known Arnoux - Rauzy sequences. This thesis represents a significant contribution to the study of Sturmian and episturmian words, and related objects such as generalized Thue - Morse words and substitutions on a finite alphabet. Specifically, we prove some new properties of certain palindromic factors of the infinite Fibonacci word; establish generalized ' singular ' decompositions of suffixes of certain morphic Sturmian words; completely describe where palindromes occur in characteristic Sturmian words; explicitly determine all integer powers occurring in a certain class of k-strict episturmian words ( including the k-bonacci word ) ; and prove that certain episturmian and generalized Thue - Morse continued fractions are transcendental. Lastly, we begin working towards a proof of a characterization of invertible substitutions on a finite alphabet, which generalizes the fact that invertible substitutions on two letters are exactly the Sturmian morphisms. | en |
| dc.description.dissertation | Thesis (Ph.D.)--School of Mathematical Sciences, 2006. | en |
| dc.format.extent | 1290797 bytes | en |
| dc.format.extent | 111612 bytes | en |
| dc.format.mimetype | application/pdf | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.uri | http://hdl.handle.net/2440/37765 | |
| dc.language.iso | en | en |
| dc.provenance | This electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exception. If you are the author of this thesis and do not wish it to be made publicly available or If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at: http://www.adelaide.edu.au/legals | en |
| dc.subject | combinatorics on words, Sturmian words, Fibonacci word, episturmian words, Tribonacci sequence, palindromic words, singular words, powers, morphisms, transcendental continued fractions, invertible substitutions | en |
| dc.title | On Sturmian and Episturmian words, and related topics | en |
| dc.type | Thesis | en |