Year: 2026
Type: preprint
Abstract: Chung, Graham, and Spiro introduced slow Fibonacci walks and used them to partition the integers $n\ge2$ into two sequences, the down-integers and the up-integers. They studied the local spacing of these two sequences and conjectured that their $\ell$-step gap sets agree for every $\ell\ge1$. We show that the conjecture fails at $\ell=4$ by proving \[ 9\in U_4\setminus D_4 . \]
Source: arXiv (Cornell University)
Author: Aliabadi, Mohsen
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7211895846
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