Square-Free Words with Square-Free Self-Shuffles
نویسندگان
چکیده
منابع مشابه
Square-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 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-...
متن کاملInfinite square-free self-shuffling words
An infinite word w is called self-shuffling, if w = ∏ ∞ i=0 UiVi = ∏ ∞ i=0 Ui = ∏ ∞ i=0 Vi for some finite words Ui, Vi. Harju [4] recently asked whether square-free self-shuffling words exist. We answer this question affirmatively.
متن کاملSquare-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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2014
ISSN: 1077-8926
DOI: 10.37236/3605