PreprintCC BY-NC-SA 4.0arXiv
An explicit connected-sum family with unbounded knot Ramsey-stick gap
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 br(J)=2. For Kn=#nJ, the connected-sum formulas yield R(Kn)≥ 7n+3 and s(Kn)≤ 5n+3.
Related
- On Simply Connected Domains Supporting an Unbounded Analytic Function with Bounded Derivative
- Hamilton-connected cores and five cycle--wheel Ramsey numbers
- Polynomial families of incident flags and explicit off-diagonal Ramsey graphs
- Explicit channels with unbounded gains in classical communication using entangled inputs
- Explicit twists of the Carlitz module and of its tensor powers with unbounded analytic rank
BibTeX
@misc{ji2026explicit,
title = {{An explicit connected-sum family with unbounded knot Ramsey-stick gap}},
author = {Meng Ji},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27488},
eprint = {2608.27488},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27488},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - An explicit connected-sum family with unbounded knot Ramsey-stick gap
AU - Meng Ji
PY - 2026
DA - 2026/08/26
PB - arXiv
DO - 10.48550/arxiv.2608.27488
UR - https://arxiv.org/abs/2608.27488
AB - 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 br(J)=2. For K_n=#^nJ, the connected-sum formulas yield R(K_n)≥ 7n+3 and s(K_n)≤ 5n+3.
ER -