Year: 2026
Type: preprint
Abstract: Let $R(K)$ and $s(K)$ denote the Ramsey number and the stick number of a knot $K$. Johnson proved that $R-s$ is unbounded on $(p-1,p)$ torus knots and asked whether other such families exist. We give an affirmative answer. We construct an explicit eight-stick alternating knot $J$ with $c(J)=6$ and $\operatorname{br}(J)=2$. For $K_n=\#^nJ$, the connected-sum formulas yield $R(K_n)\ge 7n+3$ and $s(K_n)\le 5n+3$.
Source: arXiv (Cornell University)
Author: Ji, Meng
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204791927