### 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:**
**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu
**Bryan Ek**, Rutgers University, bryan [dot] t [dot] ek {at} math [dot] rutgers [dot] edu

Title: Several Topics in Experimental Mathematics (Thesis Defense)

Speaker: **Andrew Lohr**, Rutgers University

Date: Thursday, April 5, 2018 5:00pm

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

Abstract:

First, we'll talk about the total height statistic on a certain family of random graphs. We are able to get Maple to compute moments of this statistic. Taking limits, we confirm, via elementary methods, the fact, due to David Aldous, that the limiting (scaled) distributions are all the same. Second, we'll talk about generalizations of Sister Celine's method and Gosper's algorithm for evaluating summations. For both, we greatly extend the classes of applicable functions. For the generalization of Sister Celine's method, we allow summations of arbitrary products of hypergeometric terms and linear recurrent sequences with rational coefficients. For the extension of Gosper's algorithm, we extend it from solely hypergeometric sequences to any multi-basic sequence. For both, we give numerous applications to proving, or reproving in an automated way, interesting combinatorial problems. We'll also discuss the bunk bed conjecture, showing that in some special cases that were previously unknown, the statement of the conjecture holds.

See: http://sites.math.rutgers.edu/~bte14/expmath/