Combinatorial geometry:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1995
|
| Schriftenreihe: | Wiley-interscience series in discrete mathematics and optimization
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 354 Seiten Diagramme |
| ISBN: | 0471588903 |
Internformat
MARC
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| 100 | 1 | |a Pach, János |d 1954- |e Verfasser |0 (DE-588)138916543 |4 aut | |
| 245 | 1 | 0 | |a Combinatorial geometry |c János Pach ; Pankaj K. Agarwal |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1995 | |
| 300 | |a XIII, 354 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley-interscience series in discrete mathematics and optimization | |
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| 689 | 0 | 0 | |a Kombinatorische Geometrie |0 (DE-588)4140733-7 |D s |
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| 700 | 1 | |a Agarwal, Pankaj K. |e Verfasser |0 (DE-588)117125444X |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804124977103896576 |
|---|---|
| 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-full | 516.13 |
| 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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| id | DE-604.BV010510380 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:54:14Z |
| institution | BVB |
| isbn | 0471588903 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007005739 |
| oclc_num | 246761380 |
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| owner_facet | DE-20 DE-703 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-739 DE-824 DE-83 DE-11 DE-188 |
| physical | XIII, 354 Seiten Diagramme |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Wiley |
| record_format | marc |
| 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 |
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