Even More Generalizations of van der Waerden

Derrick Stolee, UNL

Meeting Time: November 8, 2011, 2:00-2:50pm

Abstract: Earlier this semester, Katie and Derek discussed van der Waerden's theorem regarding monochromatic arithmetic progressions and a generalization to combinatorial lines. This talk will present two different generalizations of arithmetic progressions: quasi-arithmetic and pseudo-arithmetic progressions. We will also investigate the Ramsey numbers for these constructions, including exact values, lower bounds, and algorithms to find extremal colorings that avoid monochromatic quasi- or pseudo-arithmetic progressions.