2 citations · 2 across the 4 of their papers we have counts for
10 papers · 1 filter
The constant of point-line incidence constructions
Martin Balko, Adam Sheffer, Ruiwen Tang
We study a lower bound for the constant of the Szemerédi-Trotter theorem. In particular, we show that a recent infinite family of point-line configurations satisfies $I({\mathcal P…
On the Number of Discrete Chains
Eyvindur Ari Palsson, Steven Senger, Adam Sheffer
We study a generalization of Erd\H os's unit distances problem to chains of distances. Given a set of points, and a sequence of distances ,…
Sum-Product Phenomena for Planar Hypercomplex Numbers
Matthew Hase-Liu, Adam Sheffer
We study the sum-product problem for the planar hypercomplex numbers: the dual numbers and double numbers. These number systems are similar to the complex numbers, but it turns out…
A Construction for Difference Sets with Local Properties
Sara Fish, Ben Lund, Adam Sheffer
We construct finite sets of real numbers that have a small difference set and strong local properties. In particular, we construct a set of real numbers such that $|A-A|=n^…
Local Properties via Color Energy Graphs and Forbidden Configurations
Sara Fish, Cosmin Pohoata, Adam Sheffer
The local properties problem of Erdős and Shelah generalizes many Ramsey problems and some distinct distances problems. In this work, we derive a variety of new bounds for the loca…
Local Properties in Colored Graphs, Distinct Distances, and Difference Sets
Cosmin Pohoata, Adam Sheffer
We study Extremal Combinatorics problems where local properties are used to derive global properties. That is, we consider a given configuration where every small piece of the conf…