English

Palindromic sequences generated from marked morphisms

Combinatorics 2015-09-14 v2

Abstract

Fixed points u=φ(u){\bf u}=\varphi({\bf u}) of marked and primitive morphisms φ\varphi over arbitrary alphabet are considered. We show that if u{\bf u} is palindromic, i.e., its language contains infinitely many palindromes, then some power of φ\varphi has a conjugate in class P{\mathcal P}. This class was introduced by Hof, Knill, Simon (1995) in order to study palindromic morphic words. Our definitions of marked and well-marked morphisms are more general than the ones previously used by Frid (1999) or Tan (2007). As any morphism with aperiodic fixed point over binary alphabet is marked, our result generalizes the result of Tan. Labb\'e (2014) demonstrated that already on a ternary alphabet the property of morphisms to be marked is important for the validity of our theorem. The main tool used in our proof is the description of bispecial factors in fixed points of morphisms provided by Klouda (2012).

Keywords

Cite

@article{arxiv.1409.7510,
  title  = {Palindromic sequences generated from marked morphisms},
  author = {Sébastien Labbé and Edita Pelantová},
  journal= {arXiv preprint arXiv:1409.7510},
  year   = {2015}
}

Comments

18 pages, 1 figure

R2 v1 2026-06-22T06:06:31.813Z