Discrete geometry and algebraic combinatorics / [edited by] Alexander Barg and Oleg R. Musin.

Includes bibliographical references.

Plank theorems via successive inradii / K. Bezdek --
Minimal fillings of finite metric spaces: the state of the art / A. Ivanov and A. Tuzhilin --
Combinatorics and geometry of transportation polytopes: an update / J.A. de Loera and E.D. Kim --
A tree sperner lemma / A. Niedermaier, D. Rizzolo, and F.E. Su --
Cliques and cycles in distance graphs and graphs of diameters / A.M. Raigorodskii --
New bounds for equiangular lines / A. Barg and W.-H. Yu --
Formal duality and generalizations of the poisson summation formula / H. Cohyn, A. Kumar, C. Reiher, and A. Schurmann --
On constructions of semi-bent functions from bent functions / G. Cohen and S. Mesnager --
Some remarks on multiplicity codes / S. Kopparty --
Multivariate posiive definite functions on spheres / O.R. Musin.

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, USA. 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.