New Bounds on van der Waerden-type Numbers for Generalized 3-term Arithmetic Progressions

Patrick Allen, Bruce M. Landman, Holly Meeks

Let a and b be positive integers with a \leq b. An (a,b)-triple is a set {x,ax+d,bx+ 2d}, where x,d \geq 1. Define T(a,b;r) to be the least positive integer n such that any r-color…