LEADER 04750nam 2200613 450 001 9910480118403321 005 20170918210039.0 010 $a1-4704-1949-1 035 $a(CKB)3150000000020207 035 $a(EBL)3114295 035 $a(SSID)ssj0001292160 035 $a(PQKBManifestationID)11742757 035 $a(PQKBTitleCode)TC0001292160 035 $a(PQKBWorkID)11267874 035 $a(PQKB)10439759 035 $a(MiAaPQ)EBC3114295 035 $a(PPN)197102689 035 $a(EXLCZ)993150000000020207 100 $a20150416h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aDiscrete geometry and algebraic combinatorics /$fAlexander Barg, Oleg R. Musin, editors 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2014. 210 4$d©2014 215 $a1 online resource (190 p.) 225 1 $aContemporary Mathematics,$x1098-3627 ;$v625 300 $a"AMS Special Session on Discrete Geometry and Algebraic Combinatorics, January 11, 2013". 311 $a1-4704-0905-4 320 $aIncludes bibliographical references at the end of each chapters. 327 $a""Cover""; ""Title page""; ""Contents""; ""Preface""; ""Plank theorems via successive inradii""; ""1. Introduction""; ""2. Extensions to Successive Inradii""; ""3. Proof of Theorem 2.1""; ""4. Proof of Theorem 2.2""; ""5. Proof of Corollary 2.3""; ""6. The equivalence of Conjectures 1.2, ???, ???, ???, ???, and ???""; ""7. Conclusion""; ""References""; ""Minimal fillings of finite metric spaces: The state of the art""; ""1. Introduction: Length-Minimizing Connections""; ""2. Combinatorial Definition of Minimal Filling""; ""3. Parametric Minimal Fillings"" 327 $a""4. Realization of Minimal Filling as a Minimal Network""""5. Minimal Parametric Fillings and Linear Programming""; ""6. Generalized Fillings""; ""7. Formula for the Weight of Minimal Filling""; ""8. Uniqueness Problem""; ""9. Minimal Fillings of Additive and Pseudo-Additive Spaces""; ""10. Examples of Minimal Fillings""; ""11. Ratios""; ""12. Generalizations for Infinite Sets""; ""Acknowledgments""; ""References""; ""Combinatorics and geometry of transportation polytopes: An update""; ""1. Introduction""; ""2. Classical transportation polytopes (2-ways)"" 327 $a""3. Multi-way transportation polytopes""""4. Further research directions and more open problems""; ""Acknowlegements""; ""References""; ""A Tree Sperner Lemma""; ""1. Introduction""; ""2. A Tree Sperner Lemma""; ""3. Metric Trees and Segmentations""; ""4. KKM Covers of Trees""; ""5. A Fixed Point Theorem for Finite Trees""; ""6. Infinite Settings""; ""7. A KKM Theorem for Cycles""; ""References""; ""Cliques and cycles in distance graphs and graphs of diameters""; ""1. Distance graphs: definitions and motivation""; ""2. Graphs of diameters: definitions and motivation"" 327 $a""3. What is the role of cliques and cycles in geometric graphs?""""4. Counting cliques in distance graphs and graphs of diameters""; ""5. Distance graphs with exponential chromatic numbers and without cliques or cycles""; ""6. The chromatic numbers of spheres""; ""7. Counterexamples to Borsuka???s conjecture on spheres of small radii""; ""References""; ""New bounds for equiangular lines""; ""1. Introduction""; ""2. SDP bounds for equiangular lines""; ""3. Tight spherical designs of harmonic index 4 and equiangular lines""; ""References"" 327 $a""Formal duality and generalizations of the Poisson summation formula""""1. Introduction""; ""2. Poisson summation formulas and duality""; ""3. Examples""; ""4. Structure theory in the cyclic case""; ""5. Non-existence of some formal duals""; ""6. Open questions""; ""Acknowledgments""; ""References""; ""On constructions of semi-bent functions from bent functions""; ""1. Introduction""; ""2. Notation and preliminaries""; ""3. Constructions of semi-bent functions from bent functions""; ""4. Conclusion""; ""References""; ""Some remarks on multiplicity codes""; ""1. Introduction"" 327 $a""2. Multiplicity Codes"" 410 0$aContemporary mathematics (American Mathematical Society) ;$v625. 606 $aDiscrete geometry$vCongresses 606 $aCombinatorial analysis$vCongresses 608 $aElectronic books. 615 0$aDiscrete geometry 615 0$aCombinatorial analysis 676 $a516/.11 702 $aBarg$b Alexander$f1960- 702 $aMusin$b O. 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