10 papers
A Salem-Spencer-Type Construction for Large Subsets of Integer Grids with No Isosceles Right Triangles
Gyula Károlyi, Jozsef Solymosi
Let be the largest size of a subset of containing no nondegenerate isosceles right triangle. We give a modified Salem--Spencer-type construction over…
Distances in Planar Integral Point Sets
Jozsef Solymosi
We show that very small distances in a planar integral point set are essentially one-dimensional. Let P be a non-collinear set of n points in the plane, all of whose pairwise dista…
A Simple Counting Argument for Dense Linear Hypergraphs
Lior Gishboliner, József Solymosi
In connection to the Brown-ErdÅs-Sós conjecture, we give a short local averaging proof of a density theorem for linear uniform hypergraphs. Let , , and suppose…
On the number of pairwise touching cylinders in
Jozsef Solymosi, Josh Zahl
John E. Littlewood posted the question {\em ``Is it possible in 3-space for seven infinite circular cylinders of unit radius each to touch all the others? Seven is the number sugge…
Two-Distance Sets over Finite Fields
Jozsef Solymosi, Chi Hoi Yip
We study two-distance sets in standard -dimensional quadratic spaces over finite fields. In characteristic , we construct sets attaining the full Larman--Rogers--Seidel bound…
On the Turán number of the in linear hypergraphs
Jozsef Solymosi
We show a construction for dense 3-uniform linear hypergraphs without grids, improving the lower bound on its Turán number.