2012/11/06 by Goc, Daniel, Mousavi, Hamoon, Shallit, Jeffrey
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL)
paper · doi:10.48550/arxiv.1211.1301
We illustrate a general technique for enumerating factors of k-automatic sequences by proving a conjecture on the number f(n) of unbordered factors of the Thue-Morse sequence. We show that f(n) <= n for n >= 4 and that f(n) = n infinitely often. We also give examples of automatic sequences having exactly 2 unbordered factors of every length.