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arXiv · 2609.04473

A counterexample to the Chung-Graham-Spiro gap-set conjecture

Mohsen Aliabadi
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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 \[ 9\in U_4\setminus D_4 . \]

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Mohsen Aliabadi. 2026-09-03. A counterexample to the Chung-Graham-Spiro gap-set conjecture. https://arxiv.org/abs/2609.04473

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