J. Currie

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20052023

most citedA proof of Dejean's conjecture

9 citations · 47 across the 34 of their papers we have counts for

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Showing 2019 · math.COShow all

4 papers · 2 filters

math.CO2019

The Number of Threshold Words on $n$ Letters Grows Exponentially for Every $n \geq 27$

James D. Currie, Lucas Mol, Narad Rampersad

For every $n \geq 27$ , we show that the number of $n / (n - 1)^{+}$ -free words (i.e., threshold words) of length $k$ on $n$ letters grows exponentially in $k$ . This settles all but finite…

math.CO2019★ 5 cited

The repetition threshold for binary rich words

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 infin…

math.CO2019

The undirected repetition threshold

James D. Currie, Lucas Mol

For rational $1 < r \leq 2$ , an undirected $r$ -power is a word of the form $x y x^{'}$ , where $x$ is nonempty, $x^{'} \in {x, x^{R}}$ , and $∣ x y x^{'} ∣/∣ x y ∣ = r$ . The undirected repetition thr…

math.CO2019

Some further results on squarefree arithmetic progressions in infinite words

James Currie, Tero Harju, Pascal Ochem +1

In a recent paper, one of us posed three open problems concerning squarefree arithmetic progressions in infinite words. In this note we solve these problems and prove some addition…

The Number of Threshold Words on n Letters Grows Exponentially for Every n≥27

The repetition threshold for binary rich words

The undirected repetition threshold

Some further results on squarefree arithmetic progressions in infinite words

The Number of Threshold Words on $n$ Letters Grows Exponentially for Every $n \geq 27$