Enumerative Theory Of Maps

Preface. 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 color solutions. 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. Bibliography. Index.