Characterization of some binary words with few squares
نویسندگان
چکیده
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 morphic words and we give such characterizations for six types of binary words containing few distinct squares.
منابع مشابه
Binary Words with Few Squares
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.
متن کاملOverlap-Free Words and Generalizations
The study of combinatorics on words dates back at least to the beginning of the 20 century and the work of Axel Thue. Thue was the first to give an example of an infinite word over a three letter alphabet that contains no squares (identical adjacent blocks) xx. This result was eventually used to solve some longstanding open problems in algebra and has remarkable connections to other areas of ma...
متن کاملAvoiding large squares in partial words
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...
متن کاملAvoiding large squares in infinite binary words
We consider three aspects of avoiding large squares in infinite binary words. First, we construct an infinite binary word avoiding both cubes xxx and squares yy with |y| ≥ 4; our construction is somewhat simpler than the original construction of Dekking. Second, we construct an infinite binary word avoiding all squares except 0, 1, and (01); our construction is somewhat simpler than the origina...
متن کاملSquares in Binary Partial Words
In this paper, we investigate the number of positions that do not start a square, the number of square occurrences, and the number of distinct squares in binary partial words. Letting σh(n) be the maximum number of positions not starting a square for binary partial words with h holes of length n, we show that limσh(n)/n = 15/31 provided the limit of h/n is zero. Letting γh(n) be the minimum num...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Theor. Comput. Sci.
دوره 588 شماره
صفحات -
تاریخ انتشار 2015