On a conjecture about finite fixed points of morphisms

Authors:
F. Levé;G. Richomme
Affiliations:
Université de Picardie Jules Verne, LaRIA, 33, Rue Saint Leu, 80039 Amiens cedex 1, France;Université de Picardie Jules Verne, LaRIA, 33, Rue Saint Leu, 80039 Amiens cedex 1, France
Venue:
Theoretical Computer Science - Combinatorics on words
Year:
2005

Citing 6
Cited 6

On some equations in free partially commutative monoids

Theoretical Computer Science
Combinatorics of words

Handbook of formal languages, vol. 1
Partial commutation and traces

Handbook of formal languages, vol. 3
Words and special factors

Theoretical Computer Science
The Book of Traces

The Book of Traces
On two-sided infinite fixed points of morphisms

Theoretical Computer Science

Counting Ordered Patterns in Words Generated by Morphisms

Language and Automata Theory and Applications
An examination of Ohlebusch and Ukkonen's conjecture on the equivalence problem for E-pattern languages

Journal of Automata, Languages and Combinatorics
Morphically primitive words

Theoretical Computer Science
The unambiguity of segmented morphisms

Discrete Applied Mathematics
Morphic primitivity and alphabet reductions

DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
Unambiguous 1-uniform morphisms

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

A conjecture of M. Billaud is: given a word w, if, for each letter x occurring in w, the word obtained by erasing all the occurrences of x in w is a fixed point of a nontrivial morphism fx, then w is also a fixed point of a non-trivial morphism. We prove that this conjecture is equivalent to a similar one on sets of words. Using this equivalence, we solve these conjectures in the particular case where each morphism fx has only one expansive letter.