2025/09/30 by Shallit, Jeffrey, Vukusic, Ingrid
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2509.25994
Following a recent paper of Anselmo et al., we consider m × n rectangular matrices formed from the Fibonacci word, and we show that their balance properties can be solved with a finite automaton. We also generalize the result to every Sturmian characteristic word corresponding to a quadratic irrational. Finally, we also examine the analogous question for the Tribonacci word and the Thue-Morse word.