4 papers
Extensions of Autocorrelation Inequalities with Applications to Additive Combinatorics
Sara Fish, Dylan King, Steven J. Miller
In a 2019 paper, Barnard and Steinerberger show that for , the following autocorrelation inequality holds: \begin{equation*} \min_{0 \leq t \leq 1} \int_\math…
Crescent configurations in normed spaces
Sara Fish, Dylan King, Steven J. Miller +2
We study the problem of crescent configurations, posed by Erdős in 1989. A crescent configuration is a set of points in the plane such that: 1) no three points lie on a common…
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…