书目名称 | Topics in Hyperplane Arrangements, Polytopes and Box-Splines | 编辑 | Corrado De Concini,Claudio Procesi | 视频video | | 概述 | Includes supplementary material: | 丛书名称 | Universitext | 图书封面 |  | 描述 | 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 zonotopesGraduate stu | 出版日期 | Textbook 2010 | 关键词 | Area; Cohomology; Laplace transforms; Weyl algebra; differential equations; polytope; toric; matrix theory; | 版次 | 1 | doi | https://doi.org/10.1007/978-0-387-78963-7 | isbn_softcover | 978-0-387-78962-0 | isbn_ebook | 978-0-387-78963-7Series ISSN 0172-5939 Series E-ISSN 2191-6675 | issn_series | 0172-5939 | copyright | Springer Science+Business Media, LLC 2010 |
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