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Field name	Details
Dewey Class	512.5
Title	Topics in Hyperplane Arrangements, Polytopes and Box-Splines ([Ebook]) / by Corrado De Concini, Claudio Procesi.
Author	De Concini, Corrado
Added Personal Name	Procesi, Claudio. , 1941-
Other name(s)	SpringerLink (Online service)
Edition statement	1.st ed.
Publication	New York, NY : Springer , 2010.
Physical Details	XXII, 381 pages. 19 illus., 4 illus. in color. : online resource.
Series	Universitext
ISBN	9780387789637
Summary Note	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.:
Contents note	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.
System details note	Access is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-387-78963-7
Links to Related Works	Subject References: Approximations and Expansions . Cell aggregation . Differential equation . Linear and Multilinear Algebras, Matrix Theory . Manifolds and Cell Complexes (incl. Diff.Topology) . Matrix theory . Ordinary differential equations . Topological groups . Topological groups, Lie groups . Authors: author . De Concini, Corrado . Procesi, Claudio. 1941- . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 512.5 . 512.5 (DDC 23) .

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Topics in Hyperplane Arrangements, Polytopes and Box-Splines

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