Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
Title: Probability and Ramsey Theory
Speaker: Aaron Robertson, Colgate University
Date: Thursday, April 13, 2017 5:00pm
Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ
We will find a threshold function f(k;r) such that almost all r-colorings of more than f(k;r) consecutive integers admit a monochromatic k-term arithmetic progression while almost no r-colorings do if we have less than f(k;r) consecutive integers. We will then move on to investigate the distribution of the random variable X = number of monochromatic k-term arithmetic progressions in [1,n] under random coloring of each integer. It is known that X tends to a Poisson distribution as k tends to infinity. We investigate what X is for small k.