On the largest Sidon subset in a finite subset of R^N

Abstract: A set is called a Sidon set if all pairwise sums of its elements are distinct, up to the order of the summands. A classical question in additive combinatorics, related to a conjecture of Erd\H{o}s, asks how large a Sidon subset one can always find in an arbitrary finite set.

In this talk, I will present a new lower bound showing that every set of $n$ points in $\mathbb{R}^N$ contains a Sidon subset of cardinality at least $$\left(\frac{1}{3\sqrt{3}}+o(1)\right)\sqrt{n}.$$ In particular, this improves a previous lower bound of Abbott for finite sets of integers.

commutative algebracombinatoricsnumber theory

Audience: researchers in the topic

New York Number Theory Seminar

Series comments: Meeting ID: 840 6618 4717 Passcode: 304403