A solution to the Burr-Erdos problems on Ramsey completeness

Joint School of Mathematics and ACO Colloquium
Thursday, November 21, 2019 - 11:00am for 1 hour (actually 50 minutes)
Skiles 006
Jacob Fox – Stanford University – https://stanford.edu/~jacobfox/
Lutz Warnke

A sequence A of positive integers is r-Ramsey complete if for every r-coloring of A, every sufficiently large integer can be written as a sum of the elements of a monochromatic subsequence. Burr and Erdos proposed several open problems in 1985 on how sparse can an r-Ramsey complete sequence be and which polynomial sequences are r-Ramsey complete. Erdos later offered cash prizes for two of these problems. We prove a result which solves the problems of Burr and Erdos on Ramsey complete sequences. The proof uses tools from probability, combinatorics, and number theory. 

Joint work with David Conlon.