Displaying similar documents to “Reduction and irreducibility for words and tree-words”

Concerning the sum of two continua each irreducible between the same pair of points

John Kline (1925)

Fundamenta Mathematicae

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The first part of the paper answers the question whether two different continua, each irreducible between the same pair of points could have a sum irreducible between two of its points. The second part shows certain properties of continua irreducible between the same pair of points and having the above mentioned property with respect to their sum.

Study of irreducible balanced pairs for substitutive languages

Julien Bernat (2008)

RAIRO - Theoretical Informatics and Applications

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Let ℒ be a language. A balanced pair consists of two words and in ℒ which have the same number of occurrences of each letter. It is irreducible if the pairs of strict prefixes of and of the same length do not form balanced pairs. In this article, we are interested in computing the set of irreducible balanced pairs on several cases of languages. We make connections with the balanced pairs algorithm and discrete geometrical constructions related to substitutive languages. We characterize...

Efficient reductions of picture words

Franz J. Brandenburg, Jürgen Dassow (1993)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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On Christoffel classes

Jean-Pierre Borel, Christophe Reutenauer (2006)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We characterize conjugation classes of Christoffel words (equivalently of standard words) by the number of factors. We give several geometric proofs of classical results on these words and sturmian words.

Sturmian jungle (or garden?) on multiliteral alphabets

L'ubomíra Balková, Edita Pelantová, Štěpán Starosta (2010)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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The properties characterizing sturmian words are considered for words on multiliteral alphabets. We summarize various generalizations of sturmian words to multiliteral alphabets and enlarge the list of known relationships among these generalizations. We provide a new equivalent definition of rich words and make use of it in the study of generalizations of sturmian words based on palindromes. We also collect many examples of infinite words to illustrate differences in the generalized...

Two-to-one continuous images of ℕ*

Alan Dow, Geta Techanie (2005)

Fundamenta Mathematicae

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A function is two-to-one if every point in the image has exactly two inverse points. We show that every two-to-one continuous image of ℕ* is homeomorphic to ℕ* when the continuum hypothesis is assumed. We also prove that there is no irreducible two-to-one continuous function whose domain is ℕ* under the same assumption.