Palindromic complexity of codings of rotations

Authors:
A. Blondin Massé;S. Brlek;S. Labbé;L. Vuillon
Affiliations:
LaCIM, Université du Québec à Montréal, C. P. 8888 Succursale Centre-Ville, Montréal (QC), Canada H3C 3P8 and Laboratoire de mathématiques, CNRS UMR 5127, Universit&# ...;LaCIM, Université du Québec à Montréal, C. P. 8888 Succursale Centre-Ville, Montréal (QC), Canada H3C 3P8;LaCIM, Université du Québec à Montréal, C. P. 8888 Succursale Centre-Ville, Montréal (QC), Canada H3C 3P8 and LIRMM, UMR 5506 CNRS, Université Montpellier II, 34392 M ...;Laboratoire de mathématiques, CNRS UMR 5127, Université de Savoie, 73376 Le Bourget-du-lac cedex, France
Venue:
Theoretical Computer Science
Year:
2011

Citing 4
Cited 1

Episturmian words and some constructions of de Luca and Rauzy

Theoretical Computer Science
A chararcterization of sturmian words by return words

European Journal of Combinatorics
Palindromes and two-dimensional sturmian sequences

Journal of Automata, Languages and Combinatorics
Palindromic richness

European Journal of Combinatorics

Palindromic richness for languages invariant under more symmetries

Theoretical Computer Science

Quantified Score

Hi-index	5.23

Visualization

Abstract

We study the palindromic complexity of infinite words obtained by coding rotations on partitions of the unit circle by inspecting the return words. The main result is that every coding of rotations on two intervals is full, that is, it realizes the maximal palindromic complexity. As a byproduct, a slight improvement about return words in codings of rotations is obtained: every factor of a coding of rotations on two intervals has at most 4 complete return words, where the bound is realized only for a finite number of factors. We also provide a combinatorial proof for the special case of complementary-symmetric Rote sequences by considering both palindromes and antipalindromes occurring in it.