Travis Dillon

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20242026

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3 papers · 2 filters

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" $\big\{(p,q) \in \mathbb{Z}^2 : \text{$p $an d$ q$ are prime}\big\} \sub…

math.CO2024

Improved Helly numbers of product sets

Srinivas Arun, Travis Dillon

A finite family $F$ of convex sets is $k$ -intersecting in $S \subseteq R^{d}$ if the intersection of every subset of $k$ convex sets in $F$ contains a poin…

math.CO2024

Piercing intersecting convex sets

Imre Bárány, Travis Dillon, Dömötör Pálvölgyi +1

Assume two finite families $A$ and $B$ of convex sets in $R^{3}$ have the property that $A \cap B \neq = \emptyset$ for every $A \in A$ and $B\in \math…