Three Recitations on Holonomic Systems and Hypergeometric Series

A tutorial on what later became to be known as WZ theory, as well as a motivated account of the seminal Gosper algorithm.Comment: Plain Te

Automatic Enumeration of Generalized Menage Numbers

I describe an empirical-yet-rigorous, algorithm, based on Riordan's rook polynomials and the so-called C-finite ansatz, fully implemented in the accompanying Maple package (http://www.math.rutgers.edu/~zeilberg/tokhniot/MENAGES ), MENAGES, that reproduces in a few seconds, rigorously-proved enumeration theorems on permutations with restricted positions, previously proved by quite a few illustrious human mathematicians, and that can go far beyond any human attempts.Comment: 15 pages. An extended version of the last of three invited talks given by the author at the 71th Seminaire Lotharingien de Combinatoire, that took place in Bertinoro, Italy, Sept. 16-18, 201