6 papers · 1 filter
Reduced complexities for sequences over finite alphabets
John M. Campbell, James Currie, Narad Rampersad
Letting denote a finite, nonempty word, let denote the word obtained from by replacing every subword of of the form for a given charac…
Words with factor complexity and minimal critical exponent
James D. Currie
Word is the fixed point of the morphism . In 2019, Shallit and Shur showed that has factor complexity . They also showed that ${\math…
Low complexity binary words avoiding -powers
James Currie, Narad Rampersad
Rote words are infinite words that contain factors of length for every . Shallit and Shur, as well as Ollinger and Shallit, showed that there are Rote words that…
The repetition threshold for ternary rich words
James D. Currie, Lucas Mol, Jarkko Peltomäki
In 2017, Vesti proposed the problem of determining the repetition threshold for infinite rich words, i.e., for infinite words in which all factors of length contain distinc…
A small morphism giving Abelian repetition threshold less than 2
James D. Currie, Narad Rampersad
It is known that there are infinite words over finite alphabets with Abelian repetition threshold arbitrarily close to 1; however, the construction previously used involves huge al…
The analogue of overlap-freeness for the Fibonacci morphism
James D. Currie, Narad Rampersad
A -power is a non-empty word of the form , where is obtained from by erasing the last letter. A binary word is called {\em faux-bonacci} if it contains no $4…