منابع مشابه
Reversible Christoffel factorizations
We define a family of natural decompositions of Sturmian words in Christoffel words, called reversible Christoffel (RC) factorizations. They arise from the observation that two Sturmian words with the same language have (almost always) arbitrarily long Abelian equivalent prefixes. Using the three gap theorem, we prove that in each RC factorization, only 2 or 3 distinct Christoffel words may occ...
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Reversible integer mapping is essential for lossless source coding by transformation. A general matrix factorization theory for reversible integer mapping of invertible linear transforms is developed in this paper. Concepts of the integer factor and the elementary reversible matrix (ERM) for integer mapping are introduced, and two forms of ERM—triangular ERM (TERM) and single-row ERM (SERM)—are...
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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. Mathematics Subject Classification. 68R15.
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E. B. Christoffel, Gesammelte mathematische Abhandlungen, Unter Mitwirkung von A. KRAZER und G. FABER, herausgegeben von L. MAURER. Zwei Bande. B. G. Teubner, Leipzig, 1910. WHEN one turns over the pages of the collected works of a mathematician such as this one, arranged in chronological order, and notes the varied fields in which the author worked, he feels an impulse to follow the methods of...
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Discrete geometry redefines notions borrowed from Euclidean geometry creating a need for new algorithmical tools. The notion of convexity does not translate trivially, and detecting if a discrete region of the plane is convex requires a deeper analysis. To the many different approaches of digital convexity, we propose the combinatorics on words point of view, unnoticed until recently in the pat...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2013
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2013.05.042