Displaying similar documents to “The Number of Non-Isomorphic Hamiltonian Circuits in an n -Dimensional Cube”

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...

Hereditary properties of words

József Balogh, Béla Bollobás (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Let 𝒫 be a hereditary property of words, i.e., an infinite class of finite words such that every subword (block) of a word belonging to 𝒫 is also in 𝒫 . Extending the classical Morse-Hedlund theorem, we show that either 𝒫 contains at least n + 1 words of length n for every n or, for some N , it contains at most N words of length n for every n . More importantly, we prove the following quantitative extension of this result: if 𝒫 has m ≤ n words of length n then, for every k ≥ n + m , it contains at most...

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.

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.

Polynomial languages with finite antidictionaries

Arseny M. Shur (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We tackle the problem of studying which kind of functions can occur as complexity functions of formal languages of a certain type. We prove that an important narrow subclass of rational languages contains languages of polynomial complexity of any integer degree over any non-trivial alphabet.