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FIBONACCI-LIKE SEQUENCES FOR VARIANTS OF THE TOWER OF HANOI, AND CORRESPONDING GRAPHS AND GRAY CODES

Abstract : We modify the rules of the classical Tower of Hanoi puzzle in a quite natural way to get the Fibonacci sequence involved in the optimal algorithm of resolution, and show some nice properties of such a variant. In particular, we deduce from this Tower of Hanoi-Fibonacci a Gray-like code on the set of binary words without the factor 11, which has some properties intersting for itself and from which an iterative algorithm for the Tower of Hanoi-Fibonacci is obtained. Such an algorithm involves the Fibonacci substitution. Eventually, we briefly extend the study to some natural generalizations.
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https://hal.archives-ouvertes.fr/hal-03685774
Contributor : Benoît Rittaud Connect in order to contact the contributor
Submitted on : Friday, June 3, 2022 - 10:59:46 AM
Last modification on : Thursday, June 9, 2022 - 3:25:35 AM

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Rittaud2022HanoiFibonacci.pdf
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  • HAL Id : hal-03685774, version 1
  • ARXIV : 2206.03047

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Benoît Rittaud. FIBONACCI-LIKE SEQUENCES FOR VARIANTS OF THE TOWER OF HANOI, AND CORRESPONDING GRAPHS AND GRAY CODES. 2022. ⟨hal-03685774⟩

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