Enumerative Theory Of Maps: 468 (Mathematics and Its Applications, 468) - Hardcover

Liu Yanpei

Hardcover

ISBN 10: 0792355997 ISBN 13: 9780792355991

Publisher: Springer, 2000

Synopsis

Combinatorics as a branch of mathematics studies the arts of counting. Enumeration occupies the foundation of combinatorics with a large range of applications not only in mathematics itself but also in many other disciplines. It is too broad a task to write a book to show the deep development in every corner from this aspect. This monograph is intended to provide a unified theory for those related to the enumeration of maps. For enumerating maps the first thing we have to know is the sym­ metry of a map. Or in other words, we have to know its automorphism group. In general, this is an interesting, complicated, and difficult problem. In order to do this, the first problem we meet is how to make a map considered without symmetry. Since the beginning of sixties when Tutte found a way of rooting on a map, the problem has been solved. This forms the basis of the enumerative theory of maps. As soon as the problem without considering the symmetry is solved for one kind of map, the general problem with symmetry can always, in principle, be solved from what we have known about the automorphism of a polyhedron, a synonym for a map, which can be determined efficiently according to another monograph of the present author [Liu58].

About this title

Synopsis

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.

Edition details

• Publisher: Springer
• Publication date: 2000
• Language: English
• ISBN 10: 0792355997
• ISBN 13: 9780792355991
• Binding: Hardcover
• Number of pages: 422