Attractors and Combinatorics on Words
Atraktory a kombinatorika na slovech
Authors
Supervisors
Reviewers
Editors
Other contributors
Journal Title
Journal ISSN
Volume Title
Publisher
České vysoké učení technické v Praze
Czech Technical University in Prague
Czech Technical University in Prague
Date of defense
2025-09-01
Abstract
Tato práce se věnuje studiu atraktorů slov. Jde o objekt, který hraje velkou roli v oblasti datové komprese. V kombinatorice na slovech se intenzivně studují atraktory prefixů významných nekonečných slov. Zde se konkrétně věnujeme Parryho slovům, což jsou slova kódující mezery mezi beta-celými čísly v numeračních systémech s reálným základem beta. Jednoduchá Parryho slova již byla studována a pro prefixy byly nalezeny atraktory, o kterých se ale sami autoři domnívali, že nejsou minimální. Výsledkem této práce je potvrzení jejich domněnky a nalezení minimálních atraktorů (až na speciální volbu parametrů). Otevřenou otázkou zůstávaly atraktory prefixů nejednoduchých Parryho slov. Pro ně jsme nalezli minimální atraktory prefixů v binárním případě.
This work focuses on the study of string attractors. It is an object that plays a significant role in the field of data compression. In combinatorics on words, attractors of prefixes of important infinite words are intensively studied. Here, we specifically focus on Parry words, which are words encoding spaces between beta-integers in number systems with real base beta. Simple Parry words have already been studied, and attractors of prefixes have been found, but the authors themselves believed that these attractors were not minimal. The result of this work is a confirmation of their conjecture and description of minimal attractors (except for special parameter choice). The attractors of prefixes of non-simple Parry words remained an open question. For them, we found the minimal attractors of prefixes in the binary case.
This work focuses on the study of string attractors. It is an object that plays a significant role in the field of data compression. In combinatorics on words, attractors of prefixes of important infinite words are intensively studied. Here, we specifically focus on Parry words, which are words encoding spaces between beta-integers in number systems with real base beta. Simple Parry words have already been studied, and attractors of prefixes have been found, but the authors themselves believed that these attractors were not minimal. The result of this work is a confirmation of their conjecture and description of minimal attractors (except for special parameter choice). The attractors of prefixes of non-simple Parry words remained an open question. For them, we found the minimal attractors of prefixes in the binary case.
Description
Keywords
atraktor, beta-celé číslo, beta-reprezentace, beta-rozvoj, jednoduché Parryho slovo, kombinatorika na slovech, morfismus, nejednoduché Parryho slovo, Parryho číslo, Parryho slovo, Rényiho rozvoj jedničky, attractor, beta-expansion, beta-integer, beta-representation, combinatorics on words, morphism, non-simple Parry sequence, Parry number, Parry sequence, Rényi expansion of unity, simple Parry sequence
Citation
Underlying research data set URL
Permanent link
Rights/License
Vysokoškolská závěrečná práce je dílo chráněné autorským zákonem. Je možné pořizovat z něj na své náklady a pro svoji osobní potřebu výpisy, opisy a rozmnoženiny. Jeho využití musí být v souladu s autorským zákonem v platném znění.
A university thesis is a work protected by the Copyright Act of the Czech Republic. Extracts, copies and transcripts of the thesis are allowed for personal use only and at one`s own expense. The use of thesis should be in compliance with the Copyright Act.
A university thesis is a work protected by the Copyright Act of the Czech Republic. Extracts, copies and transcripts of the thesis are allowed for personal use only and at one`s own expense. The use of thesis should be in compliance with the Copyright Act.