Latin square Thue-Morse sequences are overlap-free

Rob Tompkins

The Morse-Thue binary sequence is famous for avoiding the appearance of any overlaps: strings of the form cxcxc where c has one digit and x is a string of finite (possibly zero) length. We generalize this sequence from binary to an arbitrary finite alphabet of integers based upon Latin-Squares. This leads to a tiling of our sequence by rows of the Latin-Square. The resulting sequences derived from finite length Latin-Squares do not contain any overlaps.