An Atlas of the Smaller Maps in Orientable and Nonorientable Surfaces

An Atlas of the Smaller Maps in Orientable and Nonorientable Surfaces

by David Jackson, Terry I. Visentin
     
 

ISBN-10: 1584882077

ISBN-13: 9781584882077

Pub. Date: 09/28/2000

Publisher: Taylor & Francis

An Atlas of the Smaller Maps in Orientable and Nonorientable Surfaces is the first book to provide complete collections of maps along with t heir vertex and face partitions, number of rootings, and an index numb er for cross referencing. It provides an explanation of axiomatization and encoding, and serves as an introduction to maps as a combinatoria l structure.

Overview

An Atlas of the Smaller Maps in Orientable and Nonorientable Surfaces is the first book to provide complete collections of maps along with t heir vertex and face partitions, number of rootings, and an index numb er for cross referencing. It provides an explanation of axiomatization and encoding, and serves as an introduction to maps as a combinatoria l structure. The Atlas lists the maps first by genus and number of edg es, and gives the embeddings of all graphs with at most five edges in orientable surfaces, thus presenting the genus distribution for each g raph. Exemplifying the use of the Atlas, the authors explore two subst antial conjectures with origins in mathematical physics and geometry: the Quadrangulation Conjecture and the b-Conjecture.

Product Details

ISBN-13:
9781584882077
Publisher:
Taylor & Francis
Publication date:
09/28/2000
Series:
Discrete Mathematics and Its Applications Series
Pages:
296
Product dimensions:
6.40(w) x 9.50(h) x 1.01(d)

Table of Contents

PREFACE
MAPS
INTRODUCTION
Organization of the Atlas
Further Reading
SURFACES AND MAPS
Representation of Maps and Surfaces
Examples of the Definitions
Using the Atlas
An Application of k-Realizable Partitions
THE AXIOMATIZATION AND THE ENCODING OF MAPS
Orientable Surfaces
Locally Orientable Surfaces
GENERATING SERIES AND CONJECTURES
Generating Series for Hypermaps
Specialization to Maps
The Quadrangulation Conjecture
The b-Conjecture
THE ATLAS
MAPS IN ORIENTABLE SURFACES
Genus 0 - The Sphere
Genus 1 - The Torus
Genus 2 - The Double Torus
MAPS IN NONORIENTABLE SURFACES
Genus 1 - The Projective Plane
Genus 2 - The Klein Bottle
Genus 3 - The Crosscapped Torus
Genus 4 - The Doubly Crosscapped Torus
FACE REGULAR MAPS AND HYPERMAPS
Triangulations
Quadrangulations
Hypermaps
ASSOCIATED GRAPHS AND THEIR MAPS
TABLES
NUMBERS OF ROOTED MAPS
Orientable: by Vertex and Face Partition
Nonorientable: by Vertex and Face Partition
Summarized by Edges and Vertices
NUMBERS OF UNROOTED MAPS
Orientable: by Vertex and Face Partition
Nonorientable: by Vertex and Face Partition
NONREALIZABLE PAIRS OF PARTITIONS
For Orientable Surfaces
For Nonorientable Surfaces
MAP POLYNOMIALS
b-Polynomials
Genus Distributions
BIBLIOGRAPHY
GLOSSARY
INDEX

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >