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Square-Free Shuffles of Words

2013/09/09 by Tero Harju, Harju, Tero, Mike Müller +1
Computer Science · Mathematics · #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #cs.DM #cs.FL #math.CO

paper · pdf · doi:10.48550/arxiv.1309.2137

arxiv created 2013/09/09 · arxiv updated 2013/09/10

Abstract

Let u \shuffle v denote the set of all shuffles of the words u and v. It is shown that for each integer n ≥ 3 there exists a square-free ternary word u of length n such that u\shuffle u contains a square-free word. This property is then shown to also hold for infinite words, i.e., there exists an infinite square-free word u on three letters such that u can be shuffled with itself to produce an infinite square-free word w ∈ u \shuffle u.

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