منابع مشابه
Avoiding Approximate Squares
As is well-known, Axel Thue constructed an infinite word over a 3-letter alphabet that contains no squares, that is, no nonempty subwords of the form xx. In this paper we consider a variation on this problem, where we try to avoid approximate squares, that is, subwords of the form xx where |x| = |x| and x and x are “nearly” identical.
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Least-squares and kernel-ridge / Gaussian process regression are among the foundational algorithms of statistics and machine learning. Famously, the worst-case cost of exact nonparametric regression grows cubically with the data-set size; but a growing number of approximations have been developed that estimate good solutions at lower cost. These algorithms typically return point estimators, wit...
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A finite word w is an abelian square if w = xx′ with x′ a permutation of x. In 1972, Entringer, Jackson, and Schatz proved that every binary word of length k2+6k contains an abelian square of length ≥ 2k. We use Cartesian lattice paths to characterize abelian squares in binary sequences, and construct a binary word of length q(q + 1) avoiding abelian squares of length ≥ 2 √ 2q(q + 1) or greater...
متن کاملAvoiding abelian squares in partial words
Erdös raised the question whether there exist infinite abelian squarefree words over a given alphabet, that is, words in which no two adjacent subwords are permutations of each other. It can easily be checked that no such word exists over a three-letter alphabet. However, infinite abelian square-free words have been constructed over alphabets of sizes as small as four. In this paper, we investi...
متن کاملAvoiding 2-binomial squares and cubes
Two finite words u, v are 2-binomially equivalent if, for all words x of length at most 2, the number of occurrences of x as a (scattered) subword of u is equal to the number of occurrences of x in v. This notion is a refinement of the usual abelian equivalence. A 2-binomial square is a word uv where u and v are 2-binomially equivalent. In this paper, considering pure morphic words, we prove th...
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ژورنال
عنوان ژورنال: International Journal of Foundations of Computer Science
سال: 2008
ISSN: 0129-0541,1793-6373
DOI: 10.1142/s0129054108005863