Holdings: Combinatorial geometry

Combinatorial geometry:

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Bibliographic Details
Main Authors:	Pach, János 1954- (Author), Agarwal, Pankaj K. (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Wiley 1995
Series:	Wiley-interscience series in discrete mathematics and optimization
Subjects:	Kombinatorische Geometrie
Online Access:	Inhaltsverzeichnis
Physical Description:	XIII, 354 Seiten Diagramme
ISBN:	0471588903

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MARC


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Record in the Search Index

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adam_text	Contents PREFACE xi PARTI. ARRANGEMENTS OF CONVEX SETS 1 1 Geometry of Numbers 3 Lattices 3 The Two and Four Squares Theorem 6 Exercises 9 2 Approximation of a Convex Set by Polygons 11 Dowker s Theorems 11 An Extremal Property of Ellipses 14 Approximation of a Convex Body by Polytopes 16 Exercises 18 3 Packing and Covering with Congruent Convex Discs 21 Packing of Convex Discs 21 Covering by Convex Discs 26 Between Packing and Covering 30 Exercises 33 4 Lattice Packing and Lattice Covering 37 Fary s Theorem 37 Double Lattice Packing 41 Exercises 45 5 The Method of Cell Decomposition 47 Dirichlet Voronoi Cells 47 Shadow Cells 50 Exercises 54 vii viii Contents 6 Methods of Blichfeldt and Rogers 55 Blichfeldt s Method of Enlargement 56 Rogers Simplex Bound 59 Sections of a Ball Packing 66 Exercises 68 7 Efficient Random Arrangements 71 Minkowski Hlawka Theorem 71 Dense Lattice Packigs in Space 78 Lattice Packing and Codes 80 Thin Coverings in Space 86 Exercises 90 8 Circle Packings and Planar Graphs 95 Koebe Representation Theorem 96 Lipton Tarjan Separator Theorem 99 Discrete Convex Functions 102 Exercises 110 PART II. ARRANGEMENTS OF POINTS AND LINES 9 Extremal Graph Theory 117 Forbidden Paths and Cycles 117 Forbidden Complete Subgraphs 119 Erdos Stone Theorem 125 Theorems of Ramsey and Szemeredi 129 Two Geometric Applications 133 Exercises 135 10 Repeated Distances in Space 141 Unit Distances in the Plane 141 Unit Distances in the Space 147 Uniform Hypergraphs 149 Nearly Equal Distances in the Plane 153 Distinct Distances Determined by Small Subsets of a Set 158 Exercises 163 11 Arrangement of Lines 167 Subdividing an Arrangement of Lines 168 Complexity of a Collection of Cells 175 Exercises 179 Contents ix 12 Applications of the Bounds on Incidences 183 Repeated Angles in the Plane 183 Subsets with No Repeated Distances 187 Families of Curves with Bounded Degrees of Freedom 189 Repeated Distances on a Sphere 191 Distinct Distances Determined by Points 195 Exercises 198 13 More on Repeated Distances 201 Point Sets in Convex Position 201 Point Sets in General Position 207 Minimum and Maximum Distances 210 Borsuk s Problem 216 Exercises 218 14 Geometric Graphs 223 Forbidden Geometric Subgraphs 223 Partially Ordered Sets 227 Crossing Edges 230 Crossing Number and Bisection Width 236 Exercises 239 15 Epsilon Nets and Transversals of Hypergraphs 243 Transversals and Fractional Transversals 243 Vapnik Chervonenkis Dimension 247 Range Spaces and e Nets 255 Spanning Trees of Low Stabbing Number 257 Range Searching 260 Exercises 262 16 Geometric Discrepancy 267 Method of Floating Colors 268 Discrepancy and VC Dimension 271 Method of Partial Coloring 274 Discrepancy and Integral Geometry 282 Discrepancy and e Approximation 287 Exercises 290 x Contents Hints for Exercises 293 Bibliography 319 Index of Symbols 343 Author Index 345 Subject Index 351
any_adam_object	1
author	Pach, János 1954- Agarwal, Pankaj K.
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dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	516 - Geometry
dewey-raw	516.13
dewey-search	516.13
dewey-sort	3516.13
dewey-tens	510 - Mathematics
discipline	Mathematik
format	Book
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illustrated	Not Illustrated
indexdate	2024-07-09T17:54:14Z
institution	BVB
isbn	0471588903
language	English
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physical	XIII, 354 Seiten Diagramme
publishDate	1995
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publisher	Wiley
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series2	Wiley-interscience series in discrete mathematics and optimization
spelling	Pach, János 1954- Verfasser (DE-588)138916543 aut Combinatorial geometry János Pach ; Pankaj K. Agarwal New York [u.a.] Wiley 1995 XIII, 354 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Wiley-interscience series in discrete mathematics and optimization Kombinatorische Geometrie (DE-588)4140733-7 gnd rswk-swf Kombinatorische Geometrie (DE-588)4140733-7 s DE-604 Agarwal, Pankaj K. Verfasser (DE-588)117125444X aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007005739&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Pach, János 1954- Agarwal, Pankaj K. Combinatorial geometry Kombinatorische Geometrie (DE-588)4140733-7 gnd
subject_GND	(DE-588)4140733-7
title	Combinatorial geometry
title_auth	Combinatorial geometry
title_exact_search	Combinatorial geometry
title_full	Combinatorial geometry János Pach ; Pankaj K. Agarwal
title_fullStr	Combinatorial geometry János Pach ; Pankaj K. Agarwal
title_full_unstemmed	Combinatorial geometry János Pach ; Pankaj K. Agarwal
title_short	Combinatorial geometry
title_sort	combinatorial geometry
topic	Kombinatorische Geometrie (DE-588)4140733-7 gnd
topic_facet	Kombinatorische Geometrie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007005739&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT pachjanos combinatorialgeometry AT agarwalpankajk combinatorialgeometry

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