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Experimental Mathematics Seminar

An Exploration of Nested Recurrences Using Experimental Mathematics (thesis defense)

Nathan Fox: Rutgers University

Location:  Hill 705
Date & time: Thursday, 30 March 2017 at 5:00PM - 5:11PM

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.

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