地图计数通论（英文版）

SincethefirstmonographtitledEnumerativeTheoryofMapsappearedonthesubjectconsideredin1999，manyadvanceshavebeenmadebytheauthorhimselfandthosedirectedbyhimundersuchatheoreticalfoundation.Becauseofthatbookwithmuchattentiontomapsonsurfaceofgenuszero，thismonographisinprincipleconcernedwithmapsonsurfacesofgenusnotzero.Viamaintheoreticallines，thisbookisdividedintofourpartsexceptChapter1forpreliminaries.PartonecontainsChapters2through10.Thetheoryispresentedformapsongeneralsurfacesofgenusnotnecessarytobezero.Forthetheoryonasurfaceofgenuszeroiscomprehensivelyimprovedforinvestigatingmapsonallsurfacesofgeneranotzero.ParttwoconsistsofonlyChapter11.Relationshipsareestablishedforbuildingupabridgebetweensupermapsandembeddingsofagraphviatheirautomorphismgroups.PartthreeconsistsofChapters12and13.Ageneraltheoryforfindinggenusdistributionofgraphembeddings，handlepolynomialsandcrosscappolynomialsofsupermapsareconstructedonthebasisofthejointtreemethodwhichenablesustotransformaprobleminahighdimensionalspaceintoaproblemonapolygon.Allotherchapters，i.e.，Chapters14through17，aspartfourareconcernedwithseveralaspectsofmainextensionstodistinctdirections.Anappendixservesasatlasofsupermapsoftypicalgraphsofsmallsizeonsurfacesfortheconvenienceofreaderstochecktheirunderstanding.