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:

Andrew Baxter, Rutgers University, baxter{at} math [dot] rutgers [dot] edu

Doron Zeilberger, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Experimental methods applied to the computation of integer sequences (Ph.D. Thesis Defense)

Speaker: Eric Rowland, Rutgers University

Date: Thursday, April 2, 2009 5:00pm

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

Abstract:

In this talk I'll discuss two instances of the general problem we encounter in experimental mathematics of speeding up the computation of terms in an integer sequence. The first family of sequences we consider comes from the recurrence a(n) = a(n - 1) + gcd(n, a(n - 1)), which is shown to generate primes in a certain sense. The second concerns the enumeration of binary trees avoiding a given pattern, and extensions of this problem. In each case, computing sequences quickly is intimately connected to understanding the structure of the objects generating them and being able to prove theorems about them.