Topics in Hyperplane Arrangements, Polytopes and Box-Splines
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....
Gardado en:
| Auteurs principaux: | , |
|---|---|
| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Edición: | 1. |
| Series: | Universitext
|
| Sujets: | |
| Acceso en liña: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Topics in hyperplane arrangements, polytopes and box-splines, Corrado De Concini, Claudio Procesi, 2010, New York, Springer, 1 vol. (XX-384 p.), Universitext, 978-0-387-78962-0 • Topics in Hyperplane Arrangements, Polytopes and Box-Splines, Texte imprimé, 9780387570563 |
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| 100 | 1 | |a De Concini, Corrado, |d 1949-...., |c mathématicien. | |
| 245 | 1 | 0 | |a Topics in Hyperplane Arrangements, Polytopes and Box-Splines |c by Corrado De Concini, Claudio Procesi. |
| 250 | |a 1. | ||
| 260 | |a New York, NY : |b Springer New York. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Universitext |x 2191-6675 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 1 | |a 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. | |
| 505 | 0 | |a 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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | ||
| 650 | |a Polytopes | ||
| 700 | 1 | |a Procesi, Claudio, |d 1941-...., |c algébriste. |4 aut | |
| 776 | 0 | |0 147615615 |t Topics in hyperplane arrangements, polytopes and box-splines |f Corrado De Concini, Claudio Procesi |d 2010 |c New York |n Springer |p 1 vol. (XX-384 p.) |s Universitext |z 978-0-387-78962-0 | |
| 776 | 0 | |t Topics in Hyperplane Arrangements, Polytopes and Box-Splines |b Texte imprimé |z 9780387570563 | |
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