Ramsey Theory, Integer Partitions and a New Proof of the Erdos-Szekeres Theorem

Guy Moshkovitz, Asaf Shapira

Let H be a k-uniform hypergraph whose vertices are the integers 1,...,N. We say that H contains a monotone path of length n if there are x_1 < x_2 < ... < x_{n+k-1} so that H conta…