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Topics in Hyperplane Arrangements, Polytopes and Box-Splines

  • Corrado De Concini
  • Claudio Procesi

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. Corrado De Concini, Claudio Procesi
      Pages 3-23
    3. Corrado De Concini, Claudio Procesi
      Pages 25-68
    4. Corrado De Concini, Claudio Procesi
      Pages 69-75
    5. Corrado De Concini, Claudio Procesi
      Pages 77-83
    6. Corrado De Concini, Claudio Procesi
      Pages 85-102
    7. Corrado De Concini, Claudio Procesi
      Pages 103-109
  3. The Differentiable Case

    1. Front Matter
      Pages 111-111
    2. Corrado De Concini, Claudio Procesi
      Pages 113-126
    3. Corrado De Concini, Claudio Procesi
      Pages 127-139
    4. Corrado De Concini, Claudio Procesi
      Pages 141-154
    5. Corrado De Concini, Claudio Procesi
      Pages 155-162
    6. Corrado De Concini, Claudio Procesi
      Pages 163-188
  4. The Discrete Case

    1. Front Matter
      Pages 189-189
    2. Corrado De Concini, Claudio Procesi
      Pages 191-206
    3. Corrado De Concini, Claudio Procesi
      Pages 207-240
    4. Corrado De Concini, Claudio Procesi
      Pages 241-267
    5. Corrado De Concini, Claudio Procesi
      Pages 269-275
    6. Corrado De Concini, Claudio Procesi
      Pages 277-297
  5. Approximation Theory

    1. Front Matter
      Pages 299-299
    2. Corrado De Concini, Claudio Procesi
      Pages 301-309
    3. Corrado De Concini, Claudio Procesi
      Pages 311-331
    4. Corrado De Concini, Claudio Procesi
      Pages 333-343
  6. The Wonderful Model

    1. Front Matter
      Pages 345-345
    2. Corrado De Concini, Claudio Procesi
      Pages 347-371
  7. Back Matter
    Pages 373-384

About this book

Introduction

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.

Keywords

Area Cohomology Laplace transforms Weyl algebra differential equations polytope toric

Authors and affiliations

  • Corrado De Concini
    • 1
  • Claudio Procesi
    • 2
  1. 1."La Sapienza", Dipartimento di MatematicaUniversità di RomaRomaItaly
  2. 2."La Sapienza", Dipartimento di MatematicaUniversità di RomaRomaItaly

Bibliographic information

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