On the Zero Defect Conjecture
Combinatorics
2018-01-09 v2 Formal Languages and Automata Theory
Abstract
Brlek et al. conjectured in 2008 that any fixed point of a primitive morphism with finite palindromic defect is either periodic or its palindromic defect is zero. Bucci and Vaslet disproved this conjecture in 2012 by a counterexample over ternary alphabet. We prove that the conjecture is valid on binary alphabet. We also describe a class of morphisms over multiliteral alphabet for which the conjecture still holds. The proof is based on properties of extension graphs.
Keywords
Cite
@article{arxiv.1606.05525,
title = {On the Zero Defect Conjecture},
author = {Sébastien Labbé and Edita Pelantová and Štěpán Starosta},
journal= {arXiv preprint arXiv:1606.05525},
year = {2018}
}
Comments
v1: 16 pages, 3 figures; v2: 18 pages, 3 figures