Automatic Generation of Generating Functions for Chromatic Polynomials for Grid Graphs (and more general creatures) of Fixed (but arbitrary!) Width
Combinatorics
2011-04-01 v1
Abstract
This short article, dedicated to our beloved guru Philippe FLAJOLET (1948-2011), is a case-study in computer-generated combinatorial research, where the computer, all by itself, is using the transfer-matrix method to derive (rigorously!) rational generating functions for chromatic polynomials for infinite sequences of graphs generalizing the action of taking the Cartesian product with a path of length n, n=1,2,... .
Keywords
Cite
@article{arxiv.1103.6206,
title = {Automatic Generation of Generating Functions for Chromatic Polynomials for Grid Graphs (and more general creatures) of Fixed (but arbitrary!) Width},
author = {Shalosh B. Ekhad and Jocelyn Quaintance and Doron Zeilberger},
journal= {arXiv preprint arXiv:1103.6206},
year = {2011}
}
Comments
4 pages; Accompanied by Maple package http://www.math.rutgers.edu/~zeilberg/tokhniot/KamaTzviot . Sample input and output can be obtained from: http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/tzeva.html