1 citations · 2 across the 9 of their papers we have counts for
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Mutual Borders and Overlaps
Daniel Gabric
A word is said to be \emph{bordered} if it contains a non-empty proper prefix that is also a suffix. We can naturally extend this definition to pairs of non-empty words. A pair of…
The Simplest Binary Word with Only Three Squares
Daniel Gabric, Jeffrey Shallit
We re-examine previous constructions of infinite binary words containing few distinct squares with the goal of finding the "simplest", in a certain sense. We exhibit several new co…
An inequality for the number of periods in a word
Daniel Gabric, Narad Rampersad, Jeffrey Shallit
We prove an inequality for the number of periods in a word x in terms of the length of x and its initial critical exponent. Next, we characterize all periods of the length-n prefix…
Investigating the discrepancy property of de Bruijn sequences
Daniel Gabric, Joe Sawada
The discrepancy of a binary string refers to the maximum (absolute) difference between the number of ones and the number of zeroes over all possible substrings of the given binary…
Avoidance of split overlaps
Daniel Gabric, Jeffrey Shallit
We generalize Axel Thue's familiar definition of overlaps in words, and show that there are no infinite words containing split occurrences of these generalized overlaps. Along the…