FIBONACCI-LIKE SEQUENCES FOR VARIANTS OF THE TOWER OF HANOI, AND CORRESPONDING GRAPHS AND GRAY CODES - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2022

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

Résumé

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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Dates et versions

hal-03685774 , version 1 (03-06-2022)

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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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