15 citations · 35 across the 8 of their papers we have counts for
7 papers · 1 filter
Words avoiding reversed subwords
Narad Rampersad, Jeffrey Shallit
We examine words w satisfying the following property: if x is a subword of w and |x| is at least k for some fixed k, then the reversal of x is not a subword of w.
A Generalization of Repetition Threshold
Lucian Ilie, Jeffrey Shallit
Brandenburg and (implicitly) Dejean introduced the concept of repetition threshold: the smallest real number alpha such that there exists an infinite word over a k-letter alphabet…
Avoiding large squares in infinite binary words
Narad Rampersad, Jeffrey Shallit, Ming-wei Wang
We consider three aspects of avoiding large squares in infinite binary words. First, we construct an infinite binary word avoiding both cubes xxx and squares yy with |y| >= 4; our…
Simultaneous avoidance of large squares and fractional powers in infinite binary words
Jeffrey Shallit
In 1976, Dekking showed that there exists an infinite binary word that contains neither squares yy with y >= 4 nor cubes xxx. We show that `cube' can be replaced by any fractional…
Polynomial versus Exponential Growth in Repetition-Free Binary Words
Juhani Karhumaki, Jeffrey Shallit
It is known that the number of overlap-free binary words of length n grows polynomially, while the number of cubefree binary words grows exponentially. We show that the dividing li…
Cubefree binary words avoiding long squares
Narad Rampersad, Jeffrey Shallit, Ming-wei Wang
Entringer, Jackson, and Schatz conjectured in 1974 that every infinite cubefree binary word contains arbitrarily long squares. In this paper we show this conjecture is false: there…