9 citations · 11 across the 7 of their papers we have counts for
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A proof of Dejean's conjecture
James Currie, Narad Rampersad
We prove Dejean's conjecture. Specifically, we show that Dejean's conjecture holds for the last remaining open values of n, namely 15 <= n <= 26.
Dejean's conjecture holds for n>=27
James Currie, Narad Rampersad
We show that Dejean's conjecture holds for n>=27. This brings the final resolution of the conjecture by the approach of Moulin Ollagnier within range of the computationally feasibl…
There are k-uniform cubefree binary morphisms for all k >= 0
James Currie, Narad Rampersad
A word is cubefree if it contains no non-empty subword of the form xxx. A morphism h : Sigma^* -> Sigma^* is k-uniform if h(a) has length k for all a in Sigma. A morphism is cubefr…
Cubefree words with many squares
James Currie, Narad Rampersad
We construct infinite cubefree binary words containing exponentially many distinct squares of length n. We also show that for every positive integer n, there is a cubefree binary s…
Dejean's conjecture holds for n >= 30
James Currie, Narad Rampersad
We extend Carpi's results by showing that Dejean's conjecture holds for n >= 30.
Infinite words containing squares at every position
James D. Currie, Narad Rampersad
Richomme asked the following question: what is the infimum of the real numbers > 2 such that there exists an infinite word that avoids -powers but contains arbitrarily large…