Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
Title: An Exploration of Nested Recurrences Using Experimental Mathematics (thesis defense)
Speaker: Nathan Fox, Rutgers University
Date: Monday, March 30, 2017 5:00 pm
Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ
Nested recurrence relations, such as the Hofstadter Q-recurrence Q(n)=Q(n-Q(n-1))+Q(n-Q(n-2)), have no general theory. Solutions are highly dependent on the initial conditions, and many sequences they generate are not even known to be infinite. In this talk, we will see a variety of results pertaining to sequences arising from nested recurrences. These results include a method of automatically discovering solutions of a particular form, some sequences exhibiting never-before-seen behavior, and methodology for analyzing entire families of initial conditions simultaneously.