On Abelian squares and substitutions
نویسندگان
چکیده
منابع مشابه
On Avoiding Sufficiently Long Abelian Squares
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 کاملCounting Abelian Squares
An abelian square is a nonempty string of length 2n where the last n symbols form a permutation of the first n symbols. Similarly, an abelian r’th power is a concatenation of r blocks, each of length n, where each block is a permutation of the first n symbols. In this note we point out that some familiar combinatorial identities can be interpreted in terms of abelian powers. We count the number...
متن کاملOn Abelian Circular Squares in Binary Words1
To the memory of Paul Erdd os and to his living heritage Abstract. An abelian square in a binary word is a pair of adjacent non-empty blocks of the same length, having the same number of 1s. An abelian circular square is an abelian square which is possibly wrapped around the word: the tail protruding from the right end of the word reappears at the left end. Two abelian circular squares are equi...
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 کاملWords with the Maximum Number of Abelian Squares
An abelian square is the concatenation of two words that are anagrams of one another. A word of length n can contain Θ(n) distinct factors that are abelian squares. We study infinite words such that the number of abelian square factors of length n grows quadratically with n.
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1999
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(98)00250-3