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} }
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…
8 Citations
Avoiding Abelian Powers in Partial Words
- MathematicsDevelopments in Language Theory
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It is shown, in a number of cases, that the number of abelian p-free partial words of length n with h holes over a given alphabet grows exponentially as n increases, and it is proved that the authors cannot avoid abelia pth powers under arbitrary insertion of holes in an infinite word.
Abelian Repetitions in Sturmian Words
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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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- 2013
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.
Efficient Indexes for Jumbled Pattern Matching with Constant-Sized Alphabet
- Computer ScienceAlgorithmica
- 2016
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.
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