### DIMACS Graduate Student Combinatorics Seminar Series

Title: Enumerating Honeycombs using the (Umbral) Transfer Matrix Method

Speaker: **Mohamud Mohammed**, Rutgers University

Date: Monday, October 20, 2003, 1:10 pm

Location: Hill Center, Room 525, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

We will introduce the finite (infinite) Transfer Matrix Method and apply it to some known counting problems, then we will enumerate hexagonal (honeycomb) lattice animals and derive a new sequence (a(n)) that enumerates them. Our new sequence also verifies empirically that a(n) approx. (4.6704)^n n^(theta), for small theta in fact modulo laws of small numbers.

N.B. We will be outlining a methodology for our computer to do the research.