Enumerative Theory Of Maps

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.