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A word of length 0 is called an empty word and denoted by ε.
A word of length n over an alphabet of size σ can have Θ(n2) distinct Abelian periods.
(win W_{m}^{N}) is called a word of length m with symbols ({ 0,1,2,ldots,N-1}).
By induction on the word length, and by Lemma 2.2, it is enough to show this for a word of length (2).
We present a simple and easy-to-implement O(nloglogn -time algorithm for computinloglogn -timel algorithmeriods ofor word of length n over a computingsize allhabethe
end{aligned}Due to the structure of (eta ), given a word of length (2^{j+1}-1) in ({mathcal {L}} eta )) it is necessarily a factor of (tau ^{(j)} circ tau _{x}(a)), (tau ^{(j)} circ tau _{y}(a)) or (tau ^{(j)} circ tau _{z}(a)).
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In analogy to the terminology introduced by Ma et al. (2002), we define for integers a spaced word w of length ℓ and weight k as a pair where is a 'contiguous word' of length k and is a sequence of '0' and '1' characters of length ℓ, such that there are exactly k positions i in P with.
The number of such elements is at most (O(n^3),) each of them can be written as a group word of length at most (2n+1).
A binary word of length m is said to be balanced if it contains exactly m / 2 ones and m / 2 zeros [19].
The SHORTY algorithm [20] additionally used sets of mate-pairs which were all anchored on one end to a unique word of length k, or k-mer.
Taking a particular parameter for all words of length L, we get a sample of 4 L values.
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