Square Positions and Occurrences

F. Blanchet-Sadri       Yang Jiao       John Machacek

In this paper, we investigate the number of positions starting squares and the number of square occurrences in binary partial words. We show that the ratio of the maximum number of square-free positions in a binary partial word with finite holes to the length of the word approaches 15/31 as the length approaches infinity. We also show that the ratio of the minimum number of square occurrences in a binary partial word with finite holes to its length tends to 103/187 as the length tends to infinity.