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arXiv · 2503.11322

Gap estimates for the spectrum of $m$-bonacci numbers

Anna Chiara Lai·Paola Loreti
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Abstract

We establish some results on the structure of the spectrum of $m$-bonacci numbers. More precisely, we study explicit lower bounds for the distance between elements separated by $N$ positions in the ordered spectrum. The result is further detailed in the Fibonacci and Tribonacci case. The methodology combines the combinatorial structure of $m$-bonacci words and the canonical $m$-bonacci number system.

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Anna Chiara Lai, Paola Loreti. 2025-03-14. Gap estimates for the spectrum of $m$-bonacci numbers. https://arxiv.org/abs/2503.11322

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