Sidon–Ramsey and B_h Ramsey numbers

Abstract: The Sidon--Ramsey number \(SR(k)\) is the smallest positive integer \(n\) such that every \(k\)-coloring of the set of positive integers \([1,n]\) contains two distinct unordered pairs with the same sum, all of whose elements have the same color (repetition within each pair is allowed). Equivalently, \(SR(k)\) is the first value of \(n\) for which \([1,n]\) cannot be partitioned into \(k\) Sidon sets. In this talk, we explore this parameter and its connections with Ramsey theory and additive combinatorics. We discuss the asymptotic behavior of \(SR(k)\) and two generalizations, with particular emphasis on \(B_h\)--Ramsey numbers, which extend the problem from sums of two elements to sums of \(h\) elements.

This is a joint work with Manuel A. Espinosa-García, Edgardo Roldán-Pensado and J. David Suárez.

commutative algebracombinatoricsnumber theory

Audience: researchers in the topic

New York Number Theory Seminar

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