Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
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
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.