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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Showing 2020 · math.COShow all

3 papers · 2 filters

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…

math.CO2020★ 1 cited

There are level ternary circular square-free words of length $n$ for $n \neq = 5, 7, 9, 10, 14, 17.$

James D. Currie, Jesse T. Johnson

A word is level if each letter appears in it the same number of times, plus or minus 1. We give a complete characterization of the lengths for which level ternary circular square-f…

The undirected repetition threshold and undirected pattern avoidance

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

There are level ternary circular square-free words of length n for n=5,7,9,10,14,17.

There are level ternary circular square-free words of length $n$ for $n \neq = 5, 7, 9, 10, 14, 17.$