Discrete geometry and algebraic combinatorics / / Alexander Barg, Oleg R. Musin, editors

• Record Nr.: UNINA9910820631503321
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2014; ©2014
• ISBN: 1-4704-1949-1
• Descrizione fisica: 1 online resource (190 p.)
• Collana: Contemporary Mathematics, , 1098-3627 ; ; 625
• Classificazione: 52C3552C1705B4052C1005C1037F2094B4058E17
• Disciplina: 516/.11
• Soggetti: Discrete geometry; Combinatorial analysis
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "AMS Special Session on Discrete Geometry and Algebraic Combinatorics, January 11, 2013".
• Nota di bibliografia: Includes bibliographical references at the end of each chapters.
• Nota di contenuto: ""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""; ""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)""; ""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""; ""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 Borsukâ€?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""; ""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""; ""2. Multiplicity Codes""