5 papers
Point sets determining few angles are almost contained in a line or circle
Krishnendu Bhowmick, Oliver Roche-Newton, Audie Warren
We prove a structural theorem for point sets in which determine few pinned angles. More precisely, we prove the existence of an absolute constant such that if $…
A general-position problem for planar line arrangements
Oliver Roche-Newton
For all and infinitely many , we show that there exists a set of lines in such that there are no intersecting quadruples, but for every…
More sum-product type counterexamples: products with shifts and
Oliver Roche-Newton, Carl Schildkraut, Audie Warren
Adapting the construction disproving the sum-product conjecture over present in Bloom, Sawin, Schildkraut and Zhelezov, we show the existence of a constant and ar…
Additive structure in convex sets
Thomas F. Bloom, Jakob Führer, 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 containing t…
A lower bound for the number of pinned angles determined by a Cartesian product set
Oliver Roche-Newton
We prove that, for any , the Cartesian product set determines distinct angles.