Displaying similar documents to “Sumsets of finite Beatty sequences.”

Free and non-free subgroups of the fundamental group of the Hawaiian Earrings

Andreas Zastrow (2003)

Open Mathematics

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The space which is composed by embedding countably many circles in such a way into the plane that their radii are given by a null-sequence and that they all have a common tangent point is called “The Hawaiian Earrings”. The fundamental group of this space is known to be a subgroup of the inverse limit of the finitely generated free groups, and it is known to be not free. Within the recent move of trying to get hands on the algebraic invariants of non-tame (e.g. non-triangulable) spaces...

Sequences of low arithmetical complexity

Sergey V. Avgustinovich, Julien Cassaigne, Anna E. Frid (2006)

RAIRO - Theoretical Informatics and Applications

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Arithmetical complexity of a sequence is the number of words of length that can be extracted from it according to arithmetic progressions. We study uniformly recurrent words of low arithmetical complexity and describe the family of such words having lowest complexity.

On a characteristic property of Arnoux–Rauzy sequences

Jacques Justin, Giuseppe Pirillo (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Here we give a characterization of Arnoux–Rauzy sequences by the way of the lexicographic orderings of their alphabet.

A note on a conjecture of Duval and sturmian words

Filippo Mignosi, Luca Q. Zamboni (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We prove a long standing conjecture of Duval in the special case of sturmian words.

Transcendence of numbers with an expansion in a subclass of complexity 2 + 1

Tomi Kärki (2006)

RAIRO - Theoretical Informatics and Applications

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We divide infinite sequences of subword complexity into four subclasses with respect to left and right special elements and examine the structure of the subclasses with the help of Rauzy graphs. Let ≥ 2 be an integer. If the expansion in base of a number is an Arnoux-Rauzy word, then it belongs to Subclass I and the number is known to be transcendental. We prove the transcendence of numbers with expansions in the subclasses II and III.