Andrzej Dudek, Jarosław Grytczuk, Andrzej Ruciński
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引用次数: 1
Abstract
Twins in a finite word are formed by a pair of identical subwords placed at disjoint sets of positions. We investigate the maximum length of twins in a random word over a k-letter alphabet. The obtained lower bounds for small values of k significantly improve the best estimates known in the deterministic case. Bukh and Zhou in 2016 showed that every ternary word of length n contains twins of length at least 0.34n. Our main result states that in a random ternary word of length n, with high probability, one can find twins of length at least 0.41n. In the general case of alphabets of size \(k\geqslant 3\) we obtain analogous lower bounds of the form \(\frac{1.64}{k+1}n\) which are better than the known deterministic bounds for \(k\leqslant 354\). In addition, we present similar results for multiple twins in random words.
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