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Enumerative Theory of Maps : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - Liu Yanpei

Enumerative Theory of Maps

MATHEMATICS AND ITS APPLICATIONS (KLUWER )

Hardcover ISBN: 9780792355991
Number Of Pages: 411

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This monograph provides a unified theory of maps and their enumerations. The crucial idea is to suitably decompose the given set of maps for extracting a functional equation, in order to have advantages for solving or transforming it into those that can be employed to derive as simple a formula as possible. It is shown that the foundation of the theory is for rooted planar maps, since other kinds of maps including nonrooted (or symmetrical) ones and those on general surfaces have been found to have relationships with particular types in planar cases. A number of functional equations and close formulae are discovered in an exact or asymptotic manner. Audience: This book will be of interest to college teachers, graduate students working in mathematics, especially in combinatorics and graph theory, functional and approximate analysis and algebraic systems.

Preface
Preliminariesp. 1
Outerplanar Mapsp. 47
Triangulationsp. 81
Cubic Mapsp. 117
Eulerian Mapsp. 142
Nonseparable Mapsp. 168
Simple Mapsp. 199
General Mapsp. 236
Chrosum Equationsp. 274
Polysum Equationsp. 306
Chromatic Solutionsp. 326
Stochastic Behaviorsp. 359
Bibliographyp. 392
Indexp. 407
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792355991
ISBN-10: 0792355997
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER )
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 411
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 16.51  x 3.18
Weight (kg): 0.82