Jay Pantone, Rutgers Experimental Mathematics Seminar, October 6, 2016
See part 2 at vimeo.com/185888451
Abstract: In enumerative combinatorics, it is quite common to have in hand a number of known initial terms of a combinatorial sequence whose behavior you'd like to study. In this talk we'll describe the Method of Differential Approximants, a technique that can be used to shed some light on the nature of a sequence using only some known initial terms. While these methods are, on the face of it, experimental, they often lead to rigorous proofs. We'll exhibit the usefulness of this method through a variety of combinatorial topics, including chord diagrams, permutation classes, and inversion sequences.