منابع مشابه
Square-free partial words
We say that a partial word w over an alphabet A is square-free if every factor xx of w such that x and x are compatible is either of the form ⋄a or a⋄ where ⋄ is a hole and a ∈ A. We prove that there exist uncountably many square-free partial words over a ternary alphabet with an infinite number of holes.
متن کاملRich square-free words
A word w is rich if it has |w| + 1 many distinct palindromic factors, including the empty word. A word is square-free if it does not have a factor uu, where u is a non-empty word. Pelantová and Starosta (Discrete Math. 313 (2013)) proved that every infinite rich word contains a square. We will give another proof for that result. Pelantová and Starosta denoted by r(n) the length of a longest ric...
متن کاملSquare-free Words with Square-free Self-shuffles
We answer a question of Harju: For every n > 3 there is a square-free ternary word of length n with a square-free self-shuffle.
متن کاملAbelian Square-Free Partial Words
Erdös raised the question whether there exist infinite abelian square-free words over a given alphabet (words in which no two adjacent subwords are permutations of each other). Infinite abelian square-free words have been constructed over alphabets of sizes as small as four. In this paper, we investigate the problem of avoiding abelian squares in partial words (sequences that may contain some h...
متن کاملSquare-free shuffles of words
Let u v denote the set of all shuffles of the words u and v . It is shown that for each integer n ≥ 3 there exists a square-free ternary word u of length n such that u u contains a square-free word. This property is then shown to also hold for infinite words, i.e., there exists an infinite square-free word u on three letters such that u can be shuffled with itself to produce an infinite square-...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2020
ISSN: 1077-8926
DOI: 10.37236/9264