### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Matthew Russell**, Rutgers University, russell2 {at} math [dot] rutgers [dot] edu)
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Rado Numbers: Experimental and Computational Methods

Speaker: **Kellen Myers**, Rutgers University

Date: Thursday, April 24, 2014 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

The field of Ramsey Theory is well-known for its extremely large bounds. Often a Ramsey Theoretic quantity is bounded above by an astronomical number (e.g. Graham's number) but is believed to be much smaller. This frequent over-estimation in proofs hints at how difficult it is to calculate the exact values of these quantities.

I will present a few practical techniques to compute these figures for a class of Ramsey Theoretic quantities called Rado Numbers, which are associated to Diophantine equations whose solution sets have the usual Ramsey-type property. I will describe some brute-force techniques as well as techniques involving symbolic computation, and I'll give some of the results that I have obtained in these ways (and describe those I hope to obtain in the future). This talk requires no technical knowledge or special background, although knowing basic combinatorics and a little bit about Ramsey Theory wouldn't hurt.

See: http://www.math.rutgers.edu/~russell2/expmath/