# Abelian Square-Free Partial Words

@inproceedings{BlanchetSadri2010AbelianSP,
title={Abelian Square-Free Partial Words},
author={Francine Blanchet-Sadri and Jane I. Kim and Robert Mercas and William Severa and Sean Simmons},
booktitle={LATA},
year={2010}
}
• Published in LATA 24 May 2010
• Mathematics
Erdos raised the question whether there exist infinite abelian square-free words over a given alphabet (words in which no two adjacent subwords are permutations of each other). Infinite abelian square-free words have been constructed over alphabets of sizes as small as four. In this paper, we investigate the problem of avoiding abelian squares in partial words (sequences that may contain some holes). In particular, we give lower and upper bounds for the number of letters needed to construct…
7 Citations
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Developments in Language Theory
• 2011
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• 2013
If k m denotes the maximal exponent of an abelian repetition of period m, it is proved that limsup $$k_{m}/m\ge \sqrt{5}$$ for any Sturmian word, and the equality holds for the Fibonacci infinite word.
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An index for any constant-sized alphabet is developed and extended so that the position of the leftmost occurrence of the query pattern is provided at no additional cost in the complexity; this required rather nontrivial changes in the construction algorithm.
Abelian repetitions in partial words
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• 2012

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