Coverart for item
The Resource Topics in hyperplane arrangements, polytopes and box-splines, Corrado De Concini, Claudio Procesi

Topics in hyperplane arrangements, polytopes and box-splines, Corrado De Concini, Claudio Procesi

Label
Topics in hyperplane arrangements, polytopes and box-splines
Title
Topics in hyperplane arrangements, polytopes and box-splines
Statement of responsibility
Corrado De Concini, Claudio Procesi
Creator
Contributor
Subject
Language
eng
Summary
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
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
De Concini, Corrado
Dewey number
516/.158
Index
index present
Language note
English
LC call number
QA691
LC item number
.D43 2011
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Procesi, Claudio
Series statement
Universitext
http://library.link/vocab/subjectName
  • Polytopes
  • Approximation theory
  • Transformations (Mathematics)
  • Approximation theory
  • Polytopes
  • Transformations (Mathematics)
Label
Topics in hyperplane arrangements, polytopes and box-splines, Corrado De Concini, Claudio Procesi
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
664119046
Dimensions
unknown
Extent
1 online resource (xx, 384 pages).
Form of item
online
Isbn
9780387789620
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-0-387-78963-7
http://library.link/vocab/ext/overdrive/overdriveId
978-0-387-78962-0
Specific material designation
remote
System control number
(OCoLC)664119046
Label
Topics in hyperplane arrangements, polytopes and box-splines, Corrado De Concini, Claudio Procesi
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
664119046
Dimensions
unknown
Extent
1 online resource (xx, 384 pages).
Form of item
online
Isbn
9780387789620
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-0-387-78963-7
http://library.link/vocab/ext/overdrive/overdriveId
978-0-387-78962-0
Specific material designation
remote
System control number
(OCoLC)664119046

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