Results 21 to 30 of about 359 (107)
Infinite special branches in words associated with beta-expansions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2007 A Parry number is a real number β > 1 such that the Rényi β-expansion of 1 is finite or infinite eventually periodic. If this expansion is finite, β is said to be a simple Parry number. Remind that any Pisot number is a Parry number.
Christiane Frougny +2 more
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A Classification of Trapezoidal Words [PDF]
Electronic Proceedings in Theoretical Computer Science, 2011 Trapezoidal words are finite words having at most n+1 distinct factors of length n, for every n>=0. They encompass finite Sturmian words. We distinguish trapezoidal words into two disjoint subsets: open and closed trapezoidal words. A trapezoidal word
Gabriele Fici
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Decimations and sturmian words [PDF]
RAIRO - Theoretical Informatics and Applications, 1997 Summary: Standard Sturmian infinite words have a curious property discovered by G. Rauzy. If in such a word we delete all occurrences of each letter, except every \(p\)th one, then we get the some infinite word. This property and several generalizations are studied here.
Jacques Justin, Giuseppe Pirillo
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A Ramsey characterisation of eventually periodic words
Bulletin of the London Mathematical Society, Volume 54, Issue 6, Page 2437-2455, December 2022., 2022 Abstract A factorisation x=u1u2⋯$x = u_1 u_2 \cdots$ of an infinite word x$x$ on alphabet X$X$ is called ‘monochromatic’, for a given colouring of the finite words X∗$X^*$ on alphabet X$X$, if each ui$u_i$ is the same colour. Wojcik and Zamboni proved that the word x$x$ is periodic if and only if for every finite colouring of X∗$X^*$ there is a ...
Maria‐Romina Ivan +2 more
wiley +1 more source
Permutation complexity of images of Sturmian words by marked morphisms [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 We show that the permutation complexity of the image of a Sturmian word by a binary marked morphism is $n+k$ for some constant $k$ and all lengths $n$ sufficiently large.
Adam Borchert, Narad Rampersad
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Novel Stream Ciphering Algorithm for Big Data Images Using Zeckendorf Representation
Wireless Communications and Mobile Computing, Volume 2021, Issue 1, 2021., 2021 Big data is a term used for very large data sets. Digital equipment produces vast amounts of images every day; the need for image encryption is increasingly pronounced, for example, to safeguard the privacy of the patients’ medical imaging data in cloud disk.
Liangshun Wu, Hengjin Cai, Rajesh Kaluri
wiley +1 more source
Permutation Complexity Related to the Letter Doubling Map [PDF]
Electronic Proceedings in Theoretical Computer Science, 2011 Given a countable set X (usually taken to be the natural numbers or integers), an infinite permutation, π, of X is a linear ordering of X. This paper investigates the combinatorial complexity of infinite permutations on the natural numbers associated ...
Steven Widmer
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A remark on morphic sturmian words [PDF]
RAIRO - Theoretical Informatics and Applications, 1994 Summary: This note deals with binary Sturmian words that are morphic, i.e. generated by iterating a morphism. Among these, characteristic words are a well-known subclass. We prove that for every characteristic morphic word \(x\), the four words \(ax\), \(bx\), \(abx\) and \(bax\) are morphic.
Berstel, Jean, Séébold, Patrice
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On the Lie complexity of Sturmian words
Theoretical Computer Science, 2022 Bell and Shallit recently introduced the Lie complexity of an infinite word $s$ as the function counting for each length the number of conjugacy classes of words whose elements are all factors of $s$. They proved, using algebraic techniques, that the Lie complexity is bounded above by the first difference of the factor complexity plus one; hence, it is
Alessandro De Luca 0002, Gabriele Fici
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Return words in Sturmian and episturmian words [PDF]
RAIRO - Theoretical Informatics and Applications, 2000 Summary: Considering each occurrence of a word \(w\) in a recurrent infinite word, we define the set of return words of \(w\) to be the set of all distinct words beginning with an occurrence of \(w\) and ending exactly just before the next occurrence of \(w\) in the infinite word. We give a simpler proof of the recent result (of the second author) that,
Jacques Justin, Laurent Vuillon
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