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LUCAS PERMUTATIONS AND TOGGLES ON FIBONACCI PERMUTATIONS
Keywords:
permutations, Fibonacci and Lucas sequences, toggle groupsDOI:
https://doi.org/10.17654/0972087126019Abstract
In this article, we discuss Fibonacci permutations and give a new definition of Lucas permutations. We also define toggle maps on the set of Fibonacci permutations. By using this definition, we establish a bijection between toggle group generated by these maps and permutation group $S_{F_n}$, where $F_n$ is the $n$th Fibonacci number.
Received: June 8, 2025
Revised: September 26, 2025
Accepted: October 28, 2025
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