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arXiv · 2509.25994

Balanced Fibonacci word rectangles, and beyond

Jeffrey Shallit·Ingrid Vukusic
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Abstract

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. Finally, we also examine the analogous question for the Tribonacci word and the Thue-Morse word.

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Jeffrey Shallit, Ingrid Vukusic. 2025-09-30. Balanced Fibonacci word rectangles, and beyond. https://doi.org/10.46298/dmtcs.16955

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