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. 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.
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目录
Preface Chapter 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 Chapter 2 Outerplanar Maps §2.1 Plane trees §2.2 Wintersweets §2.3 Unicyclic maps §2.4 General outerplanar maps §2.5 Notes Chapter 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 Chapter 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 Chapter 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 Chapter 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 Chapter 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 Chapter 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 Chapter 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 Chapter 10 Polysum Equations §10.1 Polysum for bitrees §10.2 Outerplanar polysums §10.3 General polysums §10.4 Nonseparable polysums §10.5 Notes Chapter 11 Chromatic Solutions §11.1 General solutions §11.2 Cubic triangles §11.3 Invariants §11.4 Four color solutions §11.5 Notes Chapter 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 Bibliography Index
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