LEADER 04577nam 22008175 450 001 9910437865703321 005 20200704081732.0 010 $a1-4419-7910-7 024 7 $a10.1007/978-1-4419-7910-0 035 $a(CKB)3400000000086002 035 $a(EBL)972660 035 $a(OCoLC)811620790 035 $a(SSID)ssj0000766977 035 $a(PQKBManifestationID)11421289 035 $a(PQKBTitleCode)TC0000766977 035 $a(PQKBWorkID)10732999 035 $a(PQKB)11646950 035 $a(DE-He213)978-1-4419-7910-0 035 $a(MiAaPQ)EBC972660 035 $a(MiAaPQ)EBC6315017 035 $a(PPN)168291258 035 $a(EXLCZ)993400000000086002 100 $a20120917d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 12$aA Course in Topological Combinatorics /$fby Mark de Longueville 205 $a1st ed. 2013. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2013. 215 $a1 online resource (244 p.) 225 1 $aUniversitext,$x0172-5939 300 $aDescription based upon print version of record. 311 $a1-4899-8826-2 311 $a1-4419-7909-3 320 $aIncludes bibliographical references and index. 327 $aPreface -- List of Symbols and Typical Notation -- 1 Fair-Division Problems -- 2 Graph-Coloring Problems -- 3 Evasiveness of Graph Properties -- 4 Embedding and Mapping Problems -- A Basic Concepts from Graph Theory -- B Crash Course in Topology -- C Partially Ordered Sets, Order Complexes, and Their Topology -- D Groups and Group Actions -- E Some Results and Applications from Smith Theory -- References -- Index. 330 $aA Course in Topological Combinatorics is the first undergraduate textbook on the field of topological combinatorics, a subject that has become an active and innovative research area in mathematics over the last thirty years with growing applications in math, computer science, and other applied areas. Topological combinatorics is concerned with solutions to combinatorial problems by applying topological tools. In most cases these solutions are very elegant and the connection between combinatorics and topology often arises as an unexpected surprise. The textbook covers topics such as fair division, graph coloring problems, evasiveness of graph properties, and embedding problems from discrete geometry. The text contains a large number of figures that support the understanding of concepts and proofs. In many cases several alternative proofs for the same result are given, and each chapter ends with a series of exercises. The extensive appendix makes the book completely self-contained. The textbook is well suited for advanced undergraduate or beginning graduate mathematics students. Previous knowledge in topology or graph theory is helpful but not necessary. The text may be used as a basis for a one- or two-semester course as well as a supplementary text for a topology or combinatorics class. 410 0$aUniversitext,$x0172-5939 606 $aCombinatorics 606 $aConvex geometry  606 $aDiscrete geometry 606 $aGraph theory 606 $aGame theory 606 $aAlgorithms 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 606 $aConvex and Discrete Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21014 606 $aGraph Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M29020 606 $aGame Theory, Economics, Social and Behav. Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13011 606 $aMathematics of Algorithmic Complexity$3https://scigraph.springernature.com/ontologies/product-market-codes/M13130 615 0$aCombinatorics. 615 0$aConvex geometry . 615 0$aDiscrete geometry. 615 0$aGraph theory. 615 0$aGame theory. 615 0$aAlgorithms. 615 14$aCombinatorics. 615 24$aConvex and Discrete Geometry. 615 24$aGraph Theory. 615 24$aGame Theory, Economics, Social and Behav. Sciences. 615 24$aMathematics of Algorithmic Complexity. 676 $a514.2 700 $ade Longueville$b Mark$4aut$4http://id.loc.gov/vocabulary/relators/aut$0518539 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910437865703321 996 $aCourse in topological combinatorics$9840677 997 $aUNINA