# Ramsey Theory Working Group

### Abstract

There are various problems in Ramsey Theory, both new and longstanding. A few examples follow: - Is it true that any sequence with at least four symbols, i.e., any sequence a_1, a_2,... with a_i\in S, |S|\geq 4, contains two blocks of the same sum and same length? (So-called 3SL problem.) - Is it true that any permutation of positive integers contains a monotone 4-term arithmetic progression? - Is it possible to order all rational numbers between 0 and 1 so that there is no 3-term arithmetic progression that is monotone in the new order? - Is it true that every 2-large set is large?