Oliver Roche-Newton

activity

20242026

collaborators

4 papers

math.CO2026

A general-position problem for planar line arrangements

Oliver Roche-Newton

For all $I^´ > 0$ and infinitely many $n \in N$ , we show that there exists a set $L$ of $n$ lines in $R^{2}$ such that there are no intersecting quadruples, but for ever…

math.NT2026

More sum-product type counterexamples: products with shifts and $AA + A$

Oliver Roche-Newton, Carl Schildkraut, Audie Warren

Adapting the construction disproving the sum-product conjecture over $R$ present in Bloom, Sawin, Schildkraut and Zhelezov, we show the existence of a constant $c > 0$ and ar…

math.CO2025

Additive structure in convex sets

Thomas F. Bloom, Jakob FÃ¼hrer, Oliver Roche-Newton

This paper considers some different measures for how additively structured a convex set can be. The main result gives a construction of a convex set $A$ containing $I^c ◯ (∣ A ∣^{3/2})$ …

math.CO2024

A lower bound for the number of pinned angles determined by a Cartesian product set

Oliver Roche-Newton

We prove that, for any $B \subset R$ , the Cartesian product set $B \times B$ determines $I^c ◯ (∣ B ∣^{2 + c})$ distinct angles.

A general-position problem for planar line arrangements

More sum-product type counterexamples: products with shifts and AA+A

Additive structure in convex sets

A lower bound for the number of pinned angles determined by a Cartesian product set

More sum-product type counterexamples: products with shifts and $AA + A$