地图计数通论

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 Quadrangulations
§4.1 Outerplanar quadrangulations
§4.2 Outerplanar quadrangulations on the disc
§4.3 Hamiltonian quadrangulations on the sphere
§4.4 Inner endless planar quadrangulations
§4.5 Quadrangulations on the projective plane
§4.6 Quadrangulations on the Klein bottle
§4.7 Notes

Chapter 5 Eulerian Maps
§5.1 Planar Eulerian maps
§5.2 Tutte formula
§5.3 Eulerian planar triangulations
§5.4 Regular Eulerian planar maps
§5.5 Eulerian maps on surfaces
§5.6 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 surfaces
§6.5 Bridgeless maps on surfaces
§6.6 Notes

Chapter 7 Simple Maps
§7.1 Loopless maps
§7.2 General simple maps
§7.3 Simple bipartite maps
§7.4 Loopless maps on surfaces
§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 Chrosums on surfaces
§9.7 Notes

Chapter 10 Polysum Equations
§10.1 Polysums for bitrees
§10.2 Outerplanar polysums
§10.3 General polysums
§10.4 Nonseparable polysums
§10.5 Polysums on surfaces
§10.6 Notes

Chapter 11 Maps via Embeddings
§11.1 Automorphism group of a graph
§11.2 Embeddings of a graph
§11.3 Super maps of a graph
§11.4 Maps from embeddings
§11.5 Notes

Chapter 12 Locally Oriented Maps
§12.1 Planar Hamiltonian maps
§12.2 Biboundary inner rooted maps
§12.3 Boundary maps
§12.4 Cubic boundary maps
§12.5 Notes

Chapter 13 Genus Polynomials of Graphs
§13.1 Joint tree model
§13.2 Layer divisions
§13.3 Graphs from smaller
§13.4 Pan-bouquets
§13.5 Notes

Chapter 14 From Rooted to Unrooted
§14.1 Symmetric relations
§14.2 An application
§14.3 Symmetric principles
§14.4 General examples
§14.5 From under graphs
§14.6 Notes

Chapter 15 From Planar to Nonplanar
§15.1 Trees with boundary
§15.2 Cutting along vertices
§15.3 Cutting along faces
§15.4 Maps with a plane base
§15.5 Vertex partition
§15.6 Notes

Chapter 16 Chromatic Solutions
§16.1 General solution
§16.2 Cubic triangles
§16.3 Invariants
§16.4 Four color solutions
§16.5 Notes

Chapter 17 Stochastic Behaviors
§17.1 Asymptotics for outerplanar maps
§17.2 The average on tree-rooted maps
§17.3 Hamiltonian circuits per map
§17.4 The asymmetry on maps
§17.5 Asymptotics via equations
§17.6 Notes

Appendix Atlas of Super Maps for Small Graphs
Ax.1 BouquetsBm, 4≥m≥1
Ax.2 Link bundles Lm, 6≥m≥3
Ax.3 Complete bipartite graphs Km,n, 4≥m, n≥3
Ax.4 Wheels Wn, 5≥n≥4
Ax.5 Triconnected cubic graphs of size in [6, 15]
Bibliography
Subject Index
Author Index