Facing Up To Arrangements
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Facing Up To Arrangements Face Count Formulas For Partitions Of Space By Hyperplanes
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Author : Thomas Zaslavsky
language : en
Publisher: American Mathematical Soc.
Release Date : 1975
Facing Up To Arrangements Face Count Formulas For Partitions Of Space By Hyperplanes written by Thomas Zaslavsky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
An arrangement of hyperplanes of Euclidean or projective d-space is a finite set of hyperplanes, together with the induced partition of the space. Given the hyperplanes of an arrangement, how can the faces of the induced partition be counted? Heretofore this question has been answered for the plane, Euclidean 3-space, hyperplanes in general position, and the d-faces of the hyperplanes through the origin in Euclidean space. In each case the numbers of k-faces depend only on the incidences between intersections of the hyperplane, even though arrangements with the same intersection incidence pattern are not in general combinatorially isomorphic. We generalize this fact by demonstrating formulas for the numbers of k-faces of all Euclidean and projective arrangements, and the numbers of bounded k-faces of the former, as functions of the (semi)lattice of intersections of the hyperplanes, not dependent on the arrangement's combinatorial type.
Arrangements Of Hyperplanes
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Author : Peter Orlik
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Arrangements Of Hyperplanes written by Peter Orlik and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
An arrangement of hyperplanes is a finite collection of codimension one affine subspaces in a finite dimensional vector space. Arrangements have emerged independently as important objects in various fields of mathematics such as combinatorics, braids, configuration spaces, representation theory, reflection groups, singularity theory, and in computer science and physics. This book is the first comprehensive study of the subject. It treats arrangements with methods from combinatorics, algebra, algebraic geometry, topology, and group actions. It emphasizes general techniques which illuminate the connections among the different aspects of the subject. Its main purpose is to lay the foundations of the theory. Consequently, it is essentially self-contained and proofs are provided. Nevertheless, there are several new results here. In particular, many theorems that were previously known only for central arrangements are proved here for the first time in completegenerality. The text provides the advanced graduate student entry into a vital and active area of research. The working mathematician will findthe book useful as a source of basic results of the theory, open problems, and a comprehensive bibliography of the subject.
Representations Of Finite Dimensional Algebras And Related Topics In Lie Theory And Geometry
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Author : Vlastimil Dlab
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Representations Of Finite Dimensional Algebras And Related Topics In Lie Theory And Geometry written by Vlastimil Dlab and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ``instructional'' workshop preceding the conference, there were also workshops on ``Commutative Algebra, Algebraic Geometry and Representation Theory'', ``Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ``Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.
Oriented Matroids
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Author : Anders Björner
language : en
Publisher: Cambridge University Press
Release Date : 1999-11-18
Oriented Matroids written by Anders Björner and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-18 with Mathematics categories.
Oriented matroids are a very natural mathematical concept which presents itself in many different guises and which has connections and applications to many different areas. These include discrete and computational geometry, combinatorics, convexity, topology, algebraic geometry, operations research, computer science and theoretical chemistry. This is the second edition of the first comprehensive, accessible account of the subject. It is intended for a diverse audience: graduate students who wish to learn the subject from scratch; researchers in the various fields of application who want to concentrate on certain aspects of the theory; specialists who need a thorough reference work; and others at academic points in between. A list of exercises and open problems ends each chapter. For the second edition, the authors have expanded the bibliography greatly to ensure that it remains comprehensive and up-to-date, and they have also added an appendix surveying research since the work was first published.
Facing Up To Scarcity
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Author : Barbara H. Fried
language : en
Publisher:
Release Date : 2020
Facing Up To Scarcity written by Barbara H. Fried and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Philosophy categories.
Barbara H. Fried presents a powerful critique of the nonconsequentialist approaches that have been dominant in recent Anglophone moral and political thought. She argues that nonconsequentialist theories have disastrous consequences in the political domain and are inadequate at dealing with conflicts of individual interests in the moral domain.
Algorithmic Aspects In Information And Management
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Author : Zhao Zhang
language : en
Publisher: Springer Nature
Release Date : 2020-08-09
Algorithmic Aspects In Information And Management written by Zhao Zhang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-09 with Computers categories.
This volume constitutes the proceedings of the 14th International Conference on Algorithmic Aspects in Information and Management, AAIM 2020, held in Jinhua, China in August 2020. The 39 full papers and 17 short papers presented were carefully reviewed and selected from 76 submissions. The papers deal with emerging important algorithmic problems with a focus on the fundamental background, theoretical technology development, and real-world applications associated with information and management analysis, modeling and data mining. Special considerations are given to algorithmic research that was motivated by real-world applications.
Algebraic Geometry Modeling In Information Theory
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Author : Edgar Martinez-Moro
language : en
Publisher: World Scientific
Release Date : 2013
Algebraic Geometry Modeling In Information Theory written by Edgar Martinez-Moro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.
Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.
Handbook Of Combinatorics Volume 1
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Author : Ronald L. Graham
language : en
Publisher: Elsevier
Release Date : 1995-12-11
Handbook Of Combinatorics Volume 1 written by Ronald L. Graham and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-12-11 with Business & Economics categories.
Handbook of Combinatorics, Volume 1 focuses on basic methods, paradigms, results, issues, and trends across the broad spectrum of combinatorics. The selection first elaborates on the basic graph theory, connectivity and network flows, and matchings and extensions. Discussions focus on stable sets and claw free graphs, nonbipartite matching, multicommodity flows and disjoint paths, minimum cost circulations and flows, special proof techniques for paths and circuits, and Hamilton paths and circuits in digraphs. The manuscript then examines coloring, stable sets, and perfect graphs and embeddings and minors. The book takes a look at random graphs, hypergraphs, partially ordered sets, and matroids. Topics include geometric lattices, structural properties, linear extensions and correlation, dimension and posets of bounded degree, hypergraphs and set systems, stability, transversals, and matchings, and phase transition. The manuscript also reviews the combinatorial number theory, point lattices, convex polytopes and related complexes, and extremal problems in combinatorial geometry. The selection is a valuable reference for researchers interested in combinatorics.
Handbook Of Combinatorics
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Author : R.L. Graham
language : en
Publisher: Elsevier
Release Date : 1995-12-11
Handbook Of Combinatorics written by R.L. Graham and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-12-11 with Computers categories.
Handbook of Combinatorics
Handbook Of Combinatorics
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Author : Ronald L. Graham
language : en
Publisher: MIT Press
Release Date : 2003-03
Handbook Of Combinatorics written by Ronald L. Graham and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03 with Computers categories.
Covers combinatorics in graph theory, theoretical computer science, optimization, and convexity theory, plus applications in operations research, electrical engineering, statistical mechanics, chemistry, molecular biology, pure mathematics, and computer science.