On a generalization of Christoffel words: epichristoffel words
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چکیده
منابع مشابه
On a generalization of Christoffel words: epichristoffel words
Sturmian sequences are well-known as the ones having minimal complexity over a 2-letter alphabet. They are also the balanced sequences over a 2-letter alphabet and the sequences describing discrete lines. They are famous and have been extensively studied since the 18th century. One of the generalization of these sequences are the episturmian sequences, introduced by A. de Luca [dL97a] and studi...
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In this article, we extend the definition of Christoffel words to directed subgraphs of the hypercubic lattice in arbitrary dimension that we call Christoffel graphs. Christoffel graphs when d = 2 correspond to well-known Christoffel words. Due to periodicity, the d-dimensional Christoffel graph can be embedded in a (d−1)-torus (a parallelogram when d = 3). We show that Christoffel graphs have ...
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In this note we present some results on the Calkin-Wilf tree of irreducible fractions, giving an insight on the duality relating it to the Stern-Brocot tree, and proving noncommutative versions of known results relating labels of the CalkinWilf trees to hyperbinary expansions of positive integers. The main tool is the Christoffel tree introduced in a paper by Berstel and de Luca.
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There is a natural involution on Christoffel words, originally studied by the second author in [dL2]. We show that it has several equivalent definitions: one of them uses the slope of the word, and changes the numerator and the denominator respectively in their inverses modulo the length; another one uses the cyclic graph allowing the construction of the word, by interpreting it in two ways (on...
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Consider to construct an in5nite sequence, or an in5nite word, from a 5nite set of letters such as each letter is distributed with “good balance,” that is, as evenly as possible, when the densities of letters are provided. Such words have been applied to many scheduling and routing problems in various areas. Concerning the balancedness of words, the notions of regularity and balanced words have...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2009
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2009.05.014