Fibonacci morphisms and Sturmian words

Séébold, Patrice

doi:10.1016/0304-3975(91)90383-d

Cited by 43 publications

(27 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Actually this result is quite natural if one thinks about the presentation of the monoid of Sturmian morphisms (see [31]). Using Theorems 3.1 and 4.1, we generalize Theorem 5.1 to episturmian words: Theorem 5.2.…”

Section: Normalized Directive Word Of An Episturmian Wordmentioning

confidence: 94%

See 1 more Smart Citation

Directive words of episturmian words: equivalences and normalization

Glen

Levé

Richomme

2008

RAIRO-Theor. Inf. Appl.

View full text Add to dashboard Cite

Episturmian morphisms constitute a powerful tool to study episturmian words. Indeed, any episturmian word can be infinitely decomposed over the set of pure episturmian morphisms. Thus, an episturmian word can be defined by one of its morphic decompositions or, equivalently, by a certain directive word. Here we characterize pairs of words directing the same episturmian word. We also propose a way to uniquely define any episturmian word through a normalization of its directive words. As a consequence of these results, we characterize episturmian words having a unique directive word.

show abstract

Section: Normalized Directive Word Of An Episturmian Wordmentioning

confidence: 94%

“…Generalizing a study of the monoid of Sturmian morphisms by Séébold [31], the third author [26] answered the question: "When do two different spinned finite words direct the same episturmian morphism?" by giving a presentation of the monoid of episturmian morphisms.…”

Section: Finite Directive-equivalent Words: Presentation Versus Blockmentioning

confidence: 99%

Directive words of episturmian words: equivalences and normalization

Glen

Levé

Richomme

2008

RAIRO-Theor. Inf. Appl.

View full text Add to dashboard Cite

show abstract

“…In [17], the monoid of invertible endomorphisms over the binary alphabet has been shown to be generated by three endomorphisms: the two Nielsen transformations and the transposition exchanging the two letters. The presentation (with infinitely many relations) for this simplest case was given in [13]. For at least three letters, the monoid of invertible endomorphisms is not finitely generated [11,18].…”

Section: Introductionmentioning

confidence: 99%

A presentation of a finitely generated submonoid of invertible endomorphisms of the free monoid

Choffrut

Holub

2015

Semigroup Forum

View full text Add to dashboard Cite

An endomorphism of the free monoid A * is invertible if it is injective and extends to an automorphism of the free group generated by A. A simple example: the endomorphism that leaves all generators A invariant except one, say a, which is mapped to ba for some other generator b. We give a monoid presentation for the submonoid generated by all such endomorphisms when a and b are taken arbitrarily. These left translations are a special case of Nielsen positive transformations: "left" because the mutiplicative constant acts on the left and "positive" because this constant belongs to the free monoid, not the free group.

show abstract

“…It is the archetype of a Sturmian word [7]. The properties of the Fibonacci infinite word have been studied extensively by many authors, see, e.g., [7,8,9,10,12,15].…”

Section: Introductionmentioning

confidence: 99%