Some results in combinatorial geometry:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
1993
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Bielefeld, Univ., Diss., 1993 |
| Physical Description: | 132 S. |
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MARC
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Record in the Search Index
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CONTENTS
INTRODUCTION 4
I SOME COMBINATORIAL PROBLEMS IN AFFINE GEOME
TRY 10
1 THE CONJECTURE OF THOMAS 11
1.1 AFLINO SPACE AND CONVEX SETS. 11
1.2 INSCRIBED AFFINE COPIES OF CONVEX BODIES. 13
1.3 INFINITESIMAL BENDINGS . 16
2 PARALLELOGRAMS AND ELLIPSES 20
2.1 TWO MORE GLOBAL RESULTS . 20
2.2 INSCRIBED AND CIRCUMSCRIBED PARALLELOGRAMS.21
2.3 PROPERTIES OF LOWNER ELLIPSES .25
2.4 A NEW PROOF OF BEHREND'S INEQUALITIES.28
3 CENTRALLY SYMMETRIC CONVEX BODIES 35
3.1 ASYMMETRY AND AFFINE-REGULAR HEXAGONS.36
3.2 PARALLELOGRAMS.41
3.3 COROLLARIES.46
4 HIGHER DIMENSIONAL RESULTS 47
4.1 MACBEATH METRIC.47
4.2 SIMPLICCS AND PARALLELOTOPES.51
5 A CONJECTURE OF A. DRESS 56
5.1 PROBLEM AND BACKGROUND.56
1
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/940992035
5.2 THEOREM AND PROOF.59
5.3 PROOFS OF LEMMAS.61
5.4 REMARKS.65
6 AN OPEN PROBLEM OF ERDOS 66
6.1 CONNECTION WITH HEILBRONN'S PROBLEM.66
6.2 A PARTIAL SOLUTION.68
6.3 UNSOLVED PROBLEMS. 73
II ON THE COHERENT STRUCTURE OF THE METRIC CONE 75
7 METRIC SPACES 76
7.1 THE METRIC CONE. 76
7.2 THE ISOMETRIC EMBEDDING AND THE TIGHT EXTENSION .77
7.3 THE METRIC POLYHEDRAL SETS. 79
8 BASIC RESULTS GL
8.1 COHERENCE.81
8.2 COHERENT COMPONENTS.82
9 COHERENT DECOMPOSITION 86
9.1 /T-GRAPHS .86
9.2 PRIME METRICS.91
9.3 A DECOMPOSITION SCHEME.93
9.4 THE COMPLEX OF THE METRIC CONE. 97
10 COMBINATORIAL STRUCTURE OF METRIC POLYHEDRAL SETS *98
10.1 ASSOCIATED ATLAS.98
10.2 LOCAL SIMILARITY.102
10.3 SUMMANDS OF POLYTOPES .104
11 GENERATION OF METRICS 106
11.1 UNION OF OVERLAPPING METRICS.106
11.2 ZERO-DISTANCE CONTRACTION.108
11.3 CARTESIAN GRAPH PRODUCTS.110
2
12 COHERENT DECOMPOSITION VIA SPLIT METRICS 113
12.1 SPLIT METRICS.113
12.2 THE ISOLATION INDICES.114
12.3 SPLIT DECOMPOSITION.120
12.4 CONJECTURES OF DRESS.123
BIBLIOGRAPHY 126
3 |
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| indexdate | 2024-10-09T16:22:09Z |
| institution | BVB |
| language | English |
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| physical | 132 S. |
| publishDate | 1993 |
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| spelling | Zeng, Zhenbing Verfasser aut Some results in combinatorial geometry vorgelegt von Zhenbing Zeng 1993 132 S. txt rdacontent n rdamedia nc rdacarrier Bielefeld, Univ., Diss., 1993 Affine Geometrie (DE-588)4141566-8 gnd rswk-swf Kombinatorische Geometrie (DE-588)4140733-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Affine Geometrie (DE-588)4141566-8 s Kombinatorische Geometrie (DE-588)4140733-7 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006041764&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zeng, Zhenbing Some results in combinatorial geometry Affine Geometrie (DE-588)4141566-8 gnd Kombinatorische Geometrie (DE-588)4140733-7 gnd |
| subject_GND | (DE-588)4141566-8 (DE-588)4140733-7 (DE-588)4113937-9 |
| title | Some results in combinatorial geometry |
| title_auth | Some results in combinatorial geometry |
| title_exact_search | Some results in combinatorial geometry |
| title_full | Some results in combinatorial geometry vorgelegt von Zhenbing Zeng |
| title_fullStr | Some results in combinatorial geometry vorgelegt von Zhenbing Zeng |
| title_full_unstemmed | Some results in combinatorial geometry vorgelegt von Zhenbing Zeng |
| title_short | Some results in combinatorial geometry |
| title_sort | some results in combinatorial geometry |
| topic | Affine Geometrie (DE-588)4141566-8 gnd Kombinatorische Geometrie (DE-588)4140733-7 gnd |
| topic_facet | Affine Geometrie Kombinatorische Geometrie Hochschulschrift |
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