James D. Currie ; Lucas Mol ; Narad Rampersad - The repetition threshold for binary rich words

dmtcs:5791 - Discrete Mathematics & Theoretical Computer Science, February 24, 2020, vol. 22 no. 1 - https://doi.org/10.23638/DMTCS-22-1-6
The repetition threshold for binary rich words

Authors: James D. Currie ; Lucas Mol ; Narad Rampersad

    A word of length $n$ is rich if it contains $n$ nonempty palindromic factors. An infinite word is rich if all of its finite factors are rich. Baranwal and Shallit produced an infinite binary rich word with critical exponent $2+\sqrt{2}/2$ ($\approx 2.707$) and conjectured that this was the least possible critical exponent for infinite binary rich words (i.e., that the repetition threshold for binary rich words is $2+\sqrt{2}/2$). In this article, we give a structure theorem for infinite binary rich words that avoid $14/5$-powers (i.e., repetitions with exponent at least 2.8). As a consequence, we deduce that the repetition threshold for binary rich words is $2+\sqrt{2}/2$, as conjectured by Baranwal and Shallit. This resolves an open problem of Vesti for the binary alphabet; the problem remains open for larger alphabets.


    Volume: vol. 22 no. 1
    Section: Analysis of Algorithms
    Published on: February 24, 2020
    Accepted on: February 24, 2020
    Submitted on: September 27, 2019
    Keywords: Mathematics - Combinatorics,Computer Science - Formal Languages and Automata Theory,68R15

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    Source : ScholeXplorer HasVersion DOI 10.48550/arxiv.1908.03169
    • 10.48550/arxiv.1908.03169
    The repetition threshold for binary rich words
    Currie, James D. ; Mol, Lucas ; Rampersad, Narad ;

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