Automatic Enumeration of Generalized Menage Numbers
Combinatorics
2014-01-07 v1
Abstract
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.
Cite
@article{arxiv.1401.1089,
title = {Automatic Enumeration of Generalized Menage Numbers},
author = {Doron Zeilberger},
journal= {arXiv preprint arXiv:1401.1089},
year = {2014}
}
Comments
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, 2013