### 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:**
**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu
**Bryan Ek**, Rutgers University, bryan [dot] t [dot] ek {at} math [dot] rutgers [dot] edu

Title: A Journey into Clusters-the Goulden-Jackson method and All That

Speaker: **Mingjia Yang**, Rutgers University

Date: Thursday, April , 2018 5:00pm

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

Abstract:

The Goulden-Jackson Cluster method is a powerful way for finding the generating function for the number of words avoiding consecutive patterns. We will first discuss this method and some of its extensions. Then we will journey on to see a nice (symmetric) generating function for the number of words that avoid the pattern 12...r that we can guess using the computer, and how to justify that by human means using the Cluster method. Time permitting, we will also discuss extension to words with a certain number of the consecutive pattern 12...r and recurrences we came up with. This is joint work with Doron Zeilberger.

See: http://sites.math.rutgers.edu/~bte14/expmath/