On a conjecture about finite fixed points of morphisms

Levé, Florence; Richomme, Gwenaël

doi:10.1016/j.tcs.2005.01.011

Cited by 12 publications

(14 citation statements)

References 15 publications

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“…for every prolix pattern α there exists a morphism φ : N * −→ N * such that, for an i ∈ var(α), φ(i) = i and yet φ(α) = α (cf., e.g., Head [4], Levé and Richomme [7]). …”

Section: Definitions and Basic Notesmentioning

confidence: 99%

Unambiguous Morphic Images of Strings

Freydenberger

Reidenbach

Schneider

2006

Int. J. Found. Comput. Sci.

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Abstract. Motivated by the research on pattern languages, we study a fundamental combinatorial question on morphisms in free semigroups: With regard to any string α over some alphabet we ask for the existence of a morphism σ such that σ(α) is unambiguous, i.e. there is no morphism ρ with ρ = σ and ρ(α) = σ(α). Our main result shows that a rich and natural class of strings is provided with unambiguous morphic images.

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“…for every prolix pattern α there exists a morphism φ : N * −→ N * such that, for an i ∈ var(α), φ(i) = i and yet φ(α) = α (cf., e.g., Head [4], Levé and Richomme [7]). …”

Section: Definitions and Basic Notesmentioning

confidence: 99%

Unambiguous Morphic Images of Strings

Freydenberger

Reidenbach

Schneider

2006

Int. J. Found. Comput. Sci.

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“…Levé and Richomme [6] provide a confirmation of the contraposition of Conjecture 13 for a special case, but, apart from that, little is known about this problem. The final result of our paper shall demonstrate that Conjecture 13 is correct if words are considered that contain each of their letters exactly twice: Theorem 14.…”

Section: Qed(claim)mentioning

confidence: 96%

Morphic Primitivity and Alphabet Reductions

Nevisi

Reidenbach

2012

Developments in Language Theory

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Abstract. An alphabet reduction is a 1-uniform morphism that maps a word to an image that contains a smaller number of different letters. In the present paper we investigate the effect of alphabet reductions on morphically primitive words, i. e., words that are not a fixed point of a nontrivial morphism. Our first main result answers a question on the existence of unambiguous alphabet reductions for such words, and our second main result establishes whether alphabet reductions can be given that preserve morphic primitivity. In addition to this, we study Billaud's Conjecture -which features a different type of alphabet reduction, but is otherwise closely related to the main subject of our paper -and prove its correctness for a special case.

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“…In general, the correctness of Conjecture 3 has not been established yet. The problem is intensively studied by Levé and Richomme [8], where it is shown to be correct for certain subclasses of N * .…”

Section: Variable Target Alphabetsmentioning

confidence: 99%