At the intersection of combinatorics on words and discrete geometry : palindromes, symmetries and tilings
type: Dataset
description: In this thesis, we explore different problems at the intersection of combinatorics on words and discrete geometry. First, we study the occurrences of palindromes in codings of rotations, a family of words including the famous Sturmian words and Rote sequences. In particular, we show that these words are full, i.e. they realize the maximal palindromic complexity. Next, we consider a new family of words called generalized pseudostandard words, which are generated by an operator called iterated pseudopalindromic closure. We present a generalization of a formula described by Justin which allows one to generate in linear (thus optimal) time a generalized pseudostandard word. The central object, the f-palindrome or pseudopalindrome, is an indicator of the symmetries in geometric objects. In the last chapters, we focus on geometric problems. More precisely, we solve two conjectures of Provençal about tilings by translation, by exploiting the presence of palindromes and local periodicity in boundary words. At the end of many chapters, different open problems and conjectures are briefly presented.
landing page: https://theses.hal.science/tel-00697886
identifier: NNT: 2011GRENM072
keyword: algorithmics
keyword: algorithmique
keyword: chemins-discrets
keyword: combinatoire-des-mots
keyword: combinatorics-on-words
keyword: discrete-geometry
keyword: discrete-paths
keyword: geometrie-discrete
keyword: infoeu-reposemanticsdoctoralthesis
keyword: infoinfo-ohcomputer-science-csother-csoh
keyword: palindromes
keyword: pavages
keyword: theses
keyword: tilings
issued: 2026-05-18T16:41:55.296248
modified: 2026-05-18T16:41:55.296254
language: fr
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

At the intersection of combinatorics on words and discrete geometry : palindromes, symmetries and tilings
type: Distribution
format: HTML
access URL: https://theses.hal.science/tel-00697886
issued: 2026-05-18T16:41:55.311836
modified: 2026-05-18T16:41:55.244858