J. Currie

activity

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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28 papers · 1 filter

math.CO2023

The analogue of overlap-freeness for the period-doubling sequence

James D. Currie

Good words are binary words avoiding factors 11 and 1001, and patterns 0000 and 00010100. We show that good words bear the same relationship to the period-doubling sequence that ov…

math.CO2022★ 3 cited

Complement Avoidance in Binary Words

James Currie, L'ubomíra Dvořaková, Pascal Ochem +3

The complement $x$ of a binary word $x$ is obtained by changing each $0$ in $x$ to $1$ and vice versa. We study infinite binary words $w$ that avoid sufficiently lar…

math.CO2022★ 1 cited

Antisquares and Critical Exponents

Aseem Baranwal, James Currie, Lucas Mol +3

The (bitwise) complement $x$ of a binary word $x$ is obtained by changing each $0$ in $x$ to $1$ and vice versa. An $antisquare$ is a nonempty word of the form…

math.CO2021

Extending Dekking's construction of an infinite binary word avoiding abelian $4$ -powers

James Currie, Lucas Mol, Narad Rampersad +1

We construct an infinite binary word with critical exponent 3 that avoids abelian 4-powers. Our method gives an algorithm to determine if certain types of morphic sequences avoid a…

math.CO2020

The undirected repetition threshold and undirected pattern avoidance

James D. Currie, Lucas Mol

For a rational number $r$ such that $1 < r \leq 2$ , an undirected $r$ -power is a word of the form $x y x^{'}$ , where the word $x$ is nonempty, the word $x^{'}$ is in ${x, x^{R}}$ , and we have…

math.CO2020

Characterization of the lengths of binary circular words containing no squares other than 00, 11, and 0101

James D. Currie, Jesse T. Johnson

We characterize exactly the lengths of binary circular words containing no squares other than 00, 11, and 0101. Key words: combinatorics on words, circular words, necklaces, square…