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math.CO2025
At most 10 cylinders mutually touch: a Ramsey-theoretic approach
Travis Dillon, Junnosuke Koizumi, Sammy Luo
Littlewood asked for the maximum number of congruent infinite cylinders that can be arranged in so that every pair touches. We improve upon the proof of the seco…
math.CO2024
The prime grid contains arbitrarily large empty polygons
Travis Dillon
This paper proves a 2017 conjecture of De Loera, La Haye, Oliveros, and Roldán-Pensado that the "prime grid" $\big\{(p,q) \in \mathbb{Z}^2 : \text{$pq$ are prime}\big\} \sub…