TY  - BOOK
AU  - De Concini,Corrado
AU  - Procesi,Claudio
ED  - SpringerLink (Online service)
TI  - Topics in Hyperplane Arrangements, Polytopes and Box-Splines
T2  - Universitext
SN  - 9780387789637
AV  - QA184-205 
U1  - 512.5 23
PY  - 2010///
CY  - New York, NY
PB  - Springer New York
KW  - Mathematics
KW  - Matrix theory
KW  - Topological Groups
KW  - Differential Equations
KW  - Cell aggregation
KW  - Linear and Multilinear Algebras, Matrix Theory
KW  - Ordinary Differential Equations
KW  - Approximations and Expansions
KW  - Manifolds and Cell Complexes (incl. Diff.Topology)
KW  - Topological Groups, Lie Groups
N1  - Preliminaries -- Polytopes -- Hyperplane Arrangements -- Fourier and Laplace Transforms -- Modules over the Weyl Algebra -- Differential and Difference Equations -- Approximation Theory I -- The Di?erentiable Case -- Splines -- RX as a D-Module -- The Function TX -- Cohomology -- Differential Equations -- The Discrete Case -- Integral Points in Polytopes -- The Partition Functions -- Toric Arrangements -- Cohomology of Toric Arrangements -- Polar Parts -- Approximation Theory -- Convolution by B(X) -- Approximation by Splines -- Stationary Subdivisions -- The Wonderful Model -- Minimal Models
N2  - 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. In its simplest form, the problem is to compute the number of ways a given nonnegative integer can be expressed as the sum of h fixed positive integers. This goes back to ancient times and was investigated by Euler, Sylvester among others; in more recent times also in the higher dimensional case of vectors. The book treats several topics in a non-systematic way to show and compare a variety of approaches to the subject. No book on the material is available in the existing literature. Key topics and features include: - Numerical analysis treatments relating this problem to the theory of box splines - Study of regular functions on hyperplane and toric arrangements via D-modules - Residue formulae for partition functions and multivariate splines - Wonderful completion of the complement of hyperplane arrangements - Theory and properties of the Tutte polynomial of a matroid and of zonotopes Graduate students as well as researchers in algebra, combinatorics and numerical analysis, will benefit from Topics in Hyperplane Arrangements, Polytopes, and Box Splines
UR  - http://148.231.10.114:2048/login?url=http://link.springer.com/book/10.1007/978-0-387-78963-7
ER  -