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arXiv · 2205.05549

Self-Similar Structure of $k$- and Biperiodic Fibonacci Words

Darby Bortz·Nicholas Cummings·Suyi Gao·Elias Jaffe·Lan Mai·Benjamin Steinhurst·Pauline Tillotson
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Abstract

Defining the biperiodic Fibonacci words as a class of words over the alphabet $\{0,1\}$, and two specializations the $k-$Fibonacci and classical Fibonacci words, we provide a self-similar decomposition of these words into overlapping words of the same type. These self-similar decompositions complement the previous literature where self-similarity was indicated but the specific structure of how the pieces interact was left undiscussed.

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Darby Bortz, Nicholas Cummings, Suyi Gao, Elias Jaffe, Lan Mai, Benjamin Steinhurst, Pauline Tillotson. 2022-05-11. Self-Similar Structure of $k$- and Biperiodic Fibonacci Words. https://arxiv.org/abs/2205.05549

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