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Fibonacci-like sequences for variants of the tower of Hanoi, and corresponding graphs and gray codes

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.

preprint2022arXivOpen access
Benoît Rittaud
math.CODiscrete Mathematicsmath.NT
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Benoît Rittaud

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