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Thursday, August 6, 2020 | History

1 edition of Polytopes: Abstract, Convex and Computational found in the catalog.

Polytopes: Abstract, Convex and Computational

by T. Bisztriczky

  • 103 Want to read
  • 19 Currently reading

Published by Springer Netherlands, Imprint, Springer in Dordrecht .
Written in English


About the Edition

The aim of this volume is to reinforce the interaction between the three main branches (abstract, convex and computational) of the theory of polytopes. The articles include contributions from many of the leading experts in the field, and their topics of concern are expositions of recent results and in-depth analyses of the development (past and future) of the subject.
The subject matter of the book ranges from algorithms for assignment and transportation problems to the introduction of a geometric theory of polyhedra which need not be convex.
With polytopes as the main topic of interest, there are articles on realizations, classifications, Eulerian posets, polyhedral subdivisions, generalized stress, the Brunn--Minkowski theory, asymptotic approximations and the computation of volumes and mixed volumes.
For researchers in applied and computational convexity, convex geometry and discrete geometry at the graduate and postgraduate levels.

Edition Notes

Other titlesProceedings of the NATO Advanced Study Institute, Scarborough, Ontario, Canada, August 20--September 3, 1993
Statementedited by T. Bisztriczky, P. McMullen, R. Schneider, A. Ivić Weiss
SeriesNATO ASI Series, Series C: Mathematical and Physical Sciences, 1389-2185 -- 440, NATO ASI series -- 440.
ContributionsMcMullen, P., Schneider, R., Weiss, A. Ivić
The Physical Object
Format[electronic resource] /
Pagination1 online resource (528 pages 1 illustration in color.).
Number of Pages528
ID Numbers
Open LibraryOL27081832M
ISBN 109401109249
ISBN 109789401109246
OCLC/WorldCa840308705

E-books. Browse e-books; Series Descriptions; Book Program; MARC Records; FAQ; Proceedings; For Authors. Journal Author Submissions; Book Author Submissions; Polytopes: Abstract, Convex and Computational, () Equidecomposable and weakly neighborly polytopes. Israel Journal of Mathematics , Combinatorial.   Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile field has an immensely rich structure and numerous applications. Barvinok demonstrates that simplicity, intuitive appeal, and the universality of applications make teaching (and learning) convexity a gratifying experience. The book will benefit both teacher and student: It is easy to understand.

Cutting a polytope is a very natural way to produce new classes of interesting polytopes. Moreover, it has been very enlightening to explore which algebraic and combinatorial properties of the original polytope are hereditary to its subpolytopes obtained by a cut. In this work, we devote our attention to all the separating hyperplanes for some given polytope (integral and convex) and study the. Abstract regular polytopes stand at the end of more than two millennia of geometrical research, which began with regular polygons and polyhedra. They are highly symmetric combinatorial structures with distinctive geometric, algebraic or topological properties; in many ways more fascinating than traditional regular polytopes and tessellations.

Abstract: The first DIMACS special year, held during –, was devoted to discrete and computational geometry. The workshops addressed the following topics: geometric complexity, probabilistic methods in discrete and computational geometry, polytopes and convex sets, arrangements, and algebraic and practical issues in geometric computation.   University Lecture Series Volume: This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centers around a special class of ideals in a polynomial ring: They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties not necessarily normal.


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Polytopes: Abstract, Convex and Computational by T. Bisztriczky Download PDF EPUB FB2

The aim of this volume is to reinforce the interaction between the three main branches (abstract, convex and computational) of the theory of polytopes. The articles include contributions from many of the leading experts in the field, and their topics of concern are expositions of recent results and in-depth analyses of the development (past and.

The aim of this volume is to reinforce the interaction between the three main branches (abstract, convex and computational) of the theory of polytopes. The articles include contributions from many of the leading experts in the field, and their topics of concern are expositions of recent results.

ISBN: OCLC Number: Notes: "Proceedings of the NATO Advanced Study Institute on Polytopes: Abstract, Convex, Computational. Buy Polytopes: Abstract, Convex and Computational (Nato Science Series C:) by Bisztriczky, T., NATO Advanced Study Institute on Polytop, Bisztriczky, Tibor (ISBN: ) from Amazon's Book Store.

Everyday low prices and free delivery on eligible : T. Bisztriczky, NATO Advanced Study Institute on Polytop.

The aim of this volume is to reinforce the interaction between the three main branches (abstract, convex and computational) of the theory of polytopes. The articles include contributions from many of the leading experts in the field, and their topics of concern are expositions of recent results and in-depth analyses of the development (past and future) of the subject.

The subject matter of the. Regular polytope examples A regular pentagon is a polygon, a two-dimensional polytope with 5 edges, represented by Schläfli symbol {5}.: A regular dodecahedron is a polyhedron, a three-dimensional polytope, with 12 pentagonal faces, represented by Schläfli symbol {5,3}.: A Polytopes: Abstract cell is a 4-polytope, a four-dimensional polytope, with dodecahedral cells, represented by Schläfli.

Polytopes: Abstract, Convex and Computational. Book. Jan ; T. Bisztriczky. McMullen. Schneider. Asia Ivić Weiss. The aim of this volume is to reinforce the interaction between the three. Balog A., Bárány I.:On the convex hull of integer points in a disc, In: Discrete and computational geometry, DIMACS Ser.

6, pp. 39–44, Amer. Math. Soc, Providence RI Google Scholar Bárány I.:Random polytopes in smooth convex bodies, Mathemat pp. 81–92 MathSciNet CrossRef zbMATH Google Scholar. Publication: SCG ' Proceedings of the ninth annual symposium on Computational geometry July Pages – This book is a state-of-the-art account of the rich interplay between combinatorics and geometry of convex polytopes and computational commutative algebra via the tool of Gröbner bases.

It is an essential introduction for those who wish to perform research in this fast-developing, interdisciplinary field. Notes on Convex Sets, Polytopes, Polyhedra, Combinatorial Topology, Voronoi Diagrams and Delaunay Triangulations Jean Gallier Abstract: Some basic mathematical tools such as convex sets, polytopes and combinatorial topology, are used quite heavily in applied elds such as geometric modeling, meshing, com-puter vision, medical imaging and robotics.

The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics.

Gritzmann and V. Klee, On the complexity of some basic problems in computational convexity. II, Volume and mixed volumes, in Polytopes: Abstract, Convex and Computational (Scarborough, ON, ), NATO Advanced Science Institute Series C Mathematical Physics Science, Vol.

(Kluwer Academic Publication, Dordrecht, ), pp. – Volume and mixed volumes -- The diameter of polytopes and related applications -- Problems -- Contributed problems -- Three problems about 4-polytopes.\/span>\"@ en\/a> ; \u00A0\u00A0\u00A0\n schema:description\/a> \" The aim of this volume is to reinforce the interaction between the three main branches (abstract, convex and computational) of.

The author presents a comprehensive introduction to convex bodies and gives full proofs for some deeper theorems. Many hints and pointers to connections with other fields are given, and an exhaustive reference list is included. Polytopes: Abstract, Convex and Computational.

January T. Bisztriczky [Show full abstract] book ranges from algorithms for assignment and transportation problems to the introduction of a. In geometry, a polyhedron (plural polyhedra or polyhedrons) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or word polyhedron comes from the Classical Greek πολύεδρον, as poly-(stem of πολύς, "many") + -hedron (form of ἕδρα, "base" or "seat").

A convex polyhedron is the convex hull of finitely many points, not all on. The papers of this volume thus display a wide panorama of connections of polytope theory with other fields. Areas such as discrete and computational geometry, linear and combinatorial optimization, and scientific computing have contributed a combination of questions, ideas, results, algorithms and, finally, computer programs.

We develop algorithms for the approximation of a convex polytope in R 3 by polytopes that are either contained in it or containing it, and that have fewer vertices or facets, respectively. The approximating polytopes achieve the best possible general.

This is an expository paper on connections between enumerative combinatorics and convex polytopes. It aims to give an essentially self-contained overview of five specific instances when enumerative combinatorics and convex polytopes arise jointly in problems whose initial formulation lies in only one of these two subjects.

The abstract polytope associated with a real convex polytope is also referred to as its face lattice. The simplest polytopes Rank abstract polytopes.This paper deals with a problem from computational convexity and its application to computer algebra.

This paper determines the complexity of computing the Minkowski sum of k convex polytopes in $\mathbb{R}^d $, which are presented either in terms of vertices or in terms of facets.

In particular, if the dimension d is fixed, the authors obtain a polynomial time algorithm for adding k polytopes. "This book is a state-of-the-art account of the rich interplay between combinatorics and geometry of convex polytopes and computational commutative algebra via the tool of Gröbner bases.

It is an essential introduction for those who wish to perform research in this fast-developing, interdisciplinary s: 3.