On subword complexity functions
نویسندگان
چکیده
منابع مشابه
On scattered subword complexity
Sequences of characters called words or strings are widely studied in combinatorics, and used in various fields of sciences (e.g. chemistry, physics, social sciences, biology [2, 3, 4, 11] etc.). The elements of a word are called letters. A contiguous part of a word (obtained by erasing a prefix or/and a suffix) is a subword or factor. If we erase arbitrary letters from a word, what is obtained...
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We prove that the minimal length of a word Sn having the property that it contains exactly Fm+2 distinct subwords of length m for 1 ≤ m ≤ n is Fn + Fn+2. Here Fn is the nth Fibonacci number defined by F1 = F2 = 1 and Fn = Fn−1 + Fn−2 for n > 2. We also give an algorithm that generates a minimal word Sn for each n ≥ 1. 1991 Mathematics Subject Classification: Primary 68R15; Secondary 05C35. 0 In...
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The subword complexity of an infinite word ξ is a function f (ξ, n) returning the number of finite subwords (factors, infixes) of length n of ξ. In the present paper we investigate infinite words for which the set of subwords occurring infinitely often is a regular language. Among these infinite words we characterise those which are eventually recurrent. Furthermore, we derive some results comp...
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We study structure of pure morphic and morphic sequences and prove the following result: the subword complexity of arbitrary morphic sequence is either Θ(n) for some k ∈ N, or is
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We begin a systematic study of the relations between subword complexity of infinite words and their power avoidance. Among other things, we show that – the Thue-Morse word has the minimum possible subword complexity over all overlapfree binary words and all (73)-power-free binary words, but not over all ( 7 3) +-power-free binary words; – the twisted Thue-Morse word has the maximum possible sub...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1984
ISSN: 0166-218X
DOI: 10.1016/0166-218x(84)90102-1