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CORR
2011
Springer

A new approach to nonrepetitive sequences

8 years 9 months ago
A new approach to nonrepetitive sequences
A sequence is nonrepetitive if it does not contain two adjacent identical blocks. The remarkable construction of Thue asserts that 3 symbols are enough to build an arbitrarily long nonrepetitive sequence. It is still not settled whether the following extension holds: for every sequence of 3-element sets L1, . . . , Ln there exists a nonrepetitive sequence s1, . . . , sn with si ∈ Li. Applying the probabilistic method one can prove that this is true for sufficiently large sets Li. We present an elementary proof that sets of size 4 suffice (confirming the best known bound [14]). The argument is a simple counting with Catalan numbers involved. Our approach is inspired by a new algorithmic proof of the Lov´asz Local Lemma due to Moser and Tardos [19] and its interpretations by Fortnow [10] and Tao [22]. The presented method has further applications to nonrepetitive games and nonrepetitive colorings of graphs.
Jaroslaw Grytczuk, Jakub Kozik, Piotr Micek
Added 13 May 2011
Updated 13 May 2011
Type Journal
Year 2011
Where CORR
Authors Jaroslaw Grytczuk, Jakub Kozik, Piotr Micek
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