Overview

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.

Full Product Details

Author:   Liu Yanpei
Publisher:   Kluwer Academic Publishers
Imprint:   Kluwer Academic Publishers
Edition:   2000 ed.
Volume:   468
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   0.824kg
ISBN:  

9780792355991

ISBN 10:   0792355997
Pages:   411
Publication Date:   31 August 2000
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Preliminaries.- §1.1 Maps.- §1.2 Polynomials on maps.- §1.3 Enufunctions.- §1.4 Polysum functions.- §1.5 The Lagrangian inversion.- §1.6 The shadow functional.- §1.7 Asymptotic estimation.- §1.8 Notes.- 2 Outerplanar Maps.- §2.1 Plane trees.- §2.2 Wintersweets.- §2.3 Unicyclic maps.- §2.4 General outerplanar maps.- §2.5 Notes.- 3 Triangulations.- §3.1 Outerplanar triangulations.- §3.2 Planar triangulations.- §3.3 Triangulations on the disc.- §3.4 Triangulations on the projective plane.- §3.5 Triangulations on the torus.- §3.6 Notes.- 4 Cubic Maps.- §4.1 Planar cubic maps.- §4.2 Bipartite cubic maps.- §4.3 Cubic Hamiltonian maps.- §4.4 Cubic maps on surfaces.- §4.5 Notes.- 5 Eulerian Maps.- §5.1 Planar Eulerian maps.- §5.2 Tutte formula.- §5.3 Planar Eulerian triangulations.- §5.4 Regular Eulerian maps.- §5.5 Notes.- 6 Nonseparable Maps.- §6.1 Outerplanar nonseparable maps.- §6.2 Eulerian nonseparable maps.- §6.3 Planar nonseparable maps.- §6.4 Nonseparable maps on the surfaces.- §6.5 Notes.- 7 Simple Maps.- §7.1 Loopless maps.- §7.2 Loopless Eulerian maps.- §7.3 General simple maps.- §7.4 Simple bipartite maps.- §7.5 Notes.- 8 General Maps.- §8.1 General planar maps.- §8.2 Planar c-nets.- §8.3 Convex polyhedra.- §8.4 Quadrangulations via c-nets.- §8.5 General maps on surfaces.- §8.6 Notes.- 9 Chrosum Equations.- §9.1 Tree equations.- §9.2 Outerplanar equations.- §9.3 General equations.- §9.4 Triangulation equations.- §9.5 Well definedness.- §9.6 Notes.- 10 Polysum Equations.- §10.1 Polysum for bitrees.- §10.2 Outerplanar polysums.- §10.3 General polysums.- §10.4 Nonseparable polysums.- §10.5 Notes.- 11 Chromatic Solutions.- §11.1 General solutions.- §11.2 Cubic triangles.- §11.3 Invariants.- §11.4 Four colorsolutions.- §11.5 Notes.- 12 Stochastic Behaviors.- §12.1 Asymptotics for outerplanar maps.- §12.2 The average of tree-rooted maps.- §12.3 Hamiltonian circuits per map.- §12.4 The asymmetry of maps.- §12.5 Asymptotics via equations.- §12.6 Notes.

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