Discrete Geometry and Algebraic Combinatorics
About this Title
Alexander Barg, University of Maryland, College Park, MD and Oleg R. Musin, University of Texas at Brownsville, Brownsville, TX, Editors
Publication: Contemporary Mathematics
Publication Year: 2014; Volume 625
ISBNs: 978-1-4704-0905-0 (print); 978-1-4704-1949-3 (online)
This volume contains the proceedings of the AMS Special Session on Discrete Geometry and Algebraic Combinatorics held on January 11, 2013, in San Diego, California.
The collection of articles in this volume is devoted to packings of metric spaces and related questions, and contains new results as well as surveys of some areas of discrete geometry. This volume consists of papers on combinatorics of transportation polytopes, including results on the diameter of graphs of such polytopes; the generalized Steiner problem and related topics of the minimal fillings theory; a survey of distance graphs and graphs of diameters, and a group of papers on applications of algebraic combinatorics to packings of metric spaces including sphere packings and topics in coding theory.
In particular, this volume presents a new approach to duality in sphere packing based on the Poisson summation formula, applications of semidefinite programming to spherical codes and equiangular lines, new results in list decoding of a family of algebraic codes, and constructions of bent and semi-bent functions.
Graduate students and research mathematicians interested in discrete geometry, sphere packing, coding theory, and semidefinite programming.
Table of Contents
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- Károly Bezdek – Plank theorems via successive inradii
- Alexandr Ivanov and Alexey Tuzhilin – Minimal fillings of finite metric spaces: The state of the art
- Jesús A. De Loera and Edward D. Kim – Combinatorics and geometry of transportation polytopes: An update
- Andrew Niedermaier, Douglas Rizzolo and Francis Edward Su – A Tree Sperner Lemma
- Andrei M. Raigorodskii – Cliques and cycles in distance graphs and graphs of diameters
- Alexander Barg and Wei-Hsuan Yu – New bounds for equiangular lines
- Henry Cohn, Abhinav Kumar, Christian Reiher and Achill Schürmann – Formal duality and generalizations of the Poisson summation formula
- Gérard Cohen and Sihem Mesnager – On constructions of semi-bent functions from bent functions
- Swastik Kopparty – Some remarks on multiplicity codes
- Oleg R. Musin – Multivariate positive definite functions on spheres