Square-Free Words with Square-Free Self-Shuffles

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Square-free Words with Square-free Self-shuffles

We answer a question of Harju: For every n > 3 there is a square-free ternary word of length n with a square-free self-shuffle.

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Square-free shuffles of words

Let u 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 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-...

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Infinite square-free self-shuffling words

An infinite word w is called self-shuffling, if w = ∏ ∞ i=0 UiVi = ∏ ∞ i=0 Ui = ∏ ∞ i=0 Vi for some finite words Ui, Vi. Harju [4] recently asked whether square-free self-shuffling words exist. We answer this question affirmatively.

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Square-free partial words

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ژورنال

عنوان ژورنال: The Electronic Journal of Combinatorics

سال: 2014

ISSN: 1077-8926

DOI: 10.37236/3605