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Balanced Fibonacci word rectangles, and beyond
Jeffrey Shallit, Ingrid Vukusic
https://arxiv.org/abs/2509.25994 https://arxiv.org/pdf/2509.25994

Balanced Fibonacci word rectangles, and beyond
Following a recent paper of Anselmo et al., we consider $m \times n$ 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.