Binary Words with Few Squares
نویسندگان
چکیده
A short proof is given for a result of Fraenkel and Simpson [Electronic J. Combinatorics 2 (1995), 159–164] stating that there exists an infinite binary word which has only three different squares u.
منابع مشابه
Characterization of some binary words with few squares
Thue proved that the factors occurring infinitely many times in square-free words over {0,1,2} avoiding the factors in {010,212} are the factors of the fixed point of the morphism 0 7→ 012, 1 7→ 02, 2 7→ 1. He similarly characterized square-free words avoiding {010,020} and {121,212} as the factors of two morphic words. In this paper, we exhibit smaller morphisms to define these two square-free...
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Well-known results on the avoidance of large squares in (full) words include the following: (1) Fraenkel and Simpson showed that we can construct an infinite binary word containing at most three distinct squares; (2) Entringer, Jackson and Schatz showed that there exists an infinite binary word avoiding all squares of the form xx such that |x| ≥ 3, and that the bound 3 is optimal; (3) Dekking s...
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عنوان ژورنال:
- Bulletin of the EATCS
دوره 89 شماره
صفحات -
تاریخ انتشار 2006