J. Currie

activity

20052009

most citedA proof of Dejean's conjecture

9 citations · 11 across the 6 of their papers we have counts for

collaborators

7 papers

math.CO2009★ 9 cited

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.

math.CO2008

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…

math.CO2008

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…

math.CO2008

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.

math.CO2008★ 2 cited

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 $α$ > 2 such that there exists an infinite word that avoids $α$ -powers but contains arbitrarily large…

math.CO2008

For each $α$ > 2 there is an infinite binary word with critical exponent $α$

James D. Currie, Narad Rampersad

For each $α > 2$ there is a binary word with critical exponent $α$ .

A proof of Dejean's conjecture

There are k-uniform cubefree binary morphisms for all k >= 0

Cubefree words with many squares

Dejean's conjecture holds for n >= 30

Infinite words containing squares at every position

For each α > 2 there is an infinite binary word with critical exponent α

For each $α$ > 2 there is an infinite binary word with critical exponent $α$