Topics in Hyperplane Arrangements, Polytopes and Box-Splines

• Main Authors: De Concini, Corrado. (Author), Procesi, Claudio. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York, 2010.
• Edition: 1.
• Series: Universitext
• Subjects: Mathematics.; Matrix theory.; Topological Groups.; Differential Equations.; Cell aggregation > Mathematics.; Linear and Multilinear Algebras, Matrix Theory.; Ordinary Differential Equations.; Approximations and Expansions.; Manifolds and Cell Complexes (incl. Diff.Topology).; Topological Groups, Lie Groups.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-78963-7

Several mathematical areas that have been developed independently over the last 30 years are brought together revolving around the computation of the number of integral points in suitable families of polytopes. The problem is formulated here in terms of partition functions and multivariate splines....

Table of Contents:

• Introduction
• I Preliminaries. 1 Polytopes. 2 Hyperplane Arrangements. 3 Fourier and Laplace Transforms. 4 Modules Over the Weyl Algebra. 5 Differential and Difference Equations. 6 Approximation Theory I
• II The Differentiable Case. 7 Splines. 8 Rx as a D-Module. 9 The function Tx. 10 Cohomology. 11 Differential Equations
• III The Discrete Case. 12 Partition Functions. 13 Toric Arrangements. 14 Cohomology of Toric Arrangements. 15 Difference Equations. 16 Applications. 17 Approximation Theory II
• IV The Wonderful Model. 18 Minimal Models.