Some Recent Results on Squarefree Words

Jean Berstel

Displaying similar documents to “Some Recent Results on Squarefree Words”

Square-free and overlap-free words

A. J. Kfoury (1988)

Banach Center Publications

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The nucleus of the free alternative algebra.

Hentzel, I.R., Peresi, L.A. (2006)

Experimental Mathematics

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Generalized sum-free subsets.

Caro, Yair (1990)

International Journal of Mathematics and Mathematical Sciences

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There are more than $2^{n / 17}$ $n$ -letter ternary square-free words.

Ekhad, Shalosh B., Zeilberger, Doron (1998)

Journal of Integer Sequences [electronic only]

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Fixed-point free maps of Euclidean spaces

R. Z. Buzyakova, A. Chigogidze (2011)

Fundamenta Mathematicae

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Our main result states that every fixed-point free continuous self-map of ℝⁿ is colorable. This result can be reformulated as follows: A continuous map f: ℝⁿ → ℝⁿ is fixed-point free iff f̃: βℝⁿ → βℝⁿ is fixed-point free. We also obtain a generalization of this fact and present some examples

On finite pattern-free sets of integers

Karl Dilcher, Lutz G. Lucht (2006)

Acta Arithmetica

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Extremal infinite overlap-free binary words.

Allouche, Jean-Paul, Currie, James, Shallit, Jeffrey (1998)

The Electronic Journal of Combinatorics [electronic only]

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Conditions on periodicity for sum-free sets.

Calkin, Neil J., Finch, Steven R. (1996)

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Partially abelian squarefree words

Robert Cori, Maria Rosaria Formisano (1990)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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The number of (2,3)-sum-free subsets of {1,...,n}

Tomasz Schoen (2001)

Acta Arithmetica

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A generator of morphisms for infinite words

Pascal Ochem (2006)

RAIRO - Theoretical Informatics and Applications

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We present an algorithm which produces, in some cases, infinite words avoiding both large fractional repetitions and a given set of finite words. We use this method to show that all the ternary patterns whose avoidability index was left open in Cassaigne's thesis are 2-avoidable. We also prove that there exist exponentially many ${\frac{7}{4}}^{+}$ -free ternary words and ${\frac{7}{5}}^{+}$ -free 4-ary words. Finally we give small morphisms for binary words containing only the squares , 1 and (01)² and for binary words...