发表机构
Clayton State University（克莱顿州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对Chung-Graham-Spiro间隙集猜想，研究人员通过证明9属于上整数的4步间隙集但不属于下整数的4步间隙集，得出该猜想在ℓ=4时不成立的结论。
AI 中文摘要
Chung、Graham和Spiro引入慢斐波那契游走（slow Fibonacci walks），将整数n≥2划分为下整数（down-integers）和上整数（up-integers）两个序列；他们研究这两个序列的局部间距，猜想对所有ℓ≥1，二者的ℓ步间隙集一致。我们通过证明9∈U₄\backslash D₄，说明该猜想在ℓ=4时不成立。
英文摘要
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 \[ 9\in U_4\setminus D_4 . \]
Comments11 pages. To appear in International Journal of Number Theory
