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This book brings together many areas of mathematics that focus on methods to compute the number of integral points in suitable families or variable polytopes. The book is written by two distinguished authors and excellent examples drive the exposition.
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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.
Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.
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Topics in Hyperplane Arrangements, Polytopes and Box-Splines.
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XX, 384 p. Softcover. Versand aus Deutschland / We dispatch from Germany via Air Mail. Einband bestoßen, daher Mängelexemplar gestempelt, sonst sehr guter Zustand. Imperfect copy due to slightly bumped cover, apart from this in very good condition. Stamped. Stamped. Universitext Sprache: Englisch. Codice articolo 7448DB
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Kartoniert / Broschiert. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. -Numerical analysis treatments relating this problem to the theory of box splines -Study of regular functions on hyperplane and toric arrangements via D-modules -Applications connecting combinatorics to index theory -Presents new applications within two ind. Codice articolo 5911267
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Topics in Hyperplane Arrangements, Polytopes and Box-Splines (Universitext)
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Topics in Hyperplane Arrangements, Polytopes and Box-Splines
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Topics in Hyperplane Arrangements, Polytopes and Box-Splines brings together many areas of research that focus on methods to compute the number of integral points in suitable families or variable polytopes. The topics introduced expand upon differential and difference equations, approximation theory, cohomology, and module theory.This book, written by two distinguished authors, engages a broad audience by proving thea strong foudation.This book may be used in the classroom setting as well as a reference for researchers. 404 pp. Englisch. Codice articolo 9780387789620
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Taschenbuch. Condizione: Neu. Neuware -Topics in Hyperplane Arrangements, Polytopes and Box-Splines brings together many areas of research that focus on methods to compute the number of integral points in suitable families or variable polytopes. The topics introduced expand upon differential and difference equations, approximation theory, cohomology, and module theory.This book, written by two distinguished authors, engages a broad audience by proving the a strong foudation. This book may be used in the classroom setting as well as a reference for researchers.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 404 pp. Englisch. Codice articolo 9780387789620
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 students as well as researchers in algebra, combinatorics and numerical analysis, will benefit from Topics in Hyperplane Arrangements, Polytopes, and Box Splines. Codice articolo 9780387789620
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