Combinatorics of finite geometries:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1997
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 193 S. graph. Darst. |
| ISBN: | 0521590140 0521599938 9780521599931 |
Internformat
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| 100 | 1 | |a Batten, Lynn M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Combinatorics of finite geometries |c Lynn Margaret Batten |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1997 | |
| 300 | |a XIV, 193 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804126547734429696 |
|---|---|
| adam_text | Contents
Preface Pase xi
Preface to the first edition xiii
1 Near linear spaces 1
1.1 Some basic concepts: consistency and dependence 1
1.2 Near linear spaces 4
1.3 New near linear spaces from old 6
1.4 Dimension 9
1.5 Incidence matrices 11
1.6 The connection number 14
1.7 Linear functions 17
1.8 Exercises 19
2 Linear spaces 23
2.1 Examples 23
2.2 The de Bruijn Erdos theorem 25
2.3 Numerical properties 27
2.4 The exchange property 30
2.5 Hyperplanes 32
2.6 Linear functions 34
2.7 Exercises 37
3 Projective spaces 41
3.1 Projective planes 41
3.2 Finite projective planes 43
3.3 Embedding a near linear space in a projective plane 44
3.4 Subplanes 45
3.5 Collineations in projective planes 46
3.6 The Desargues configuration 49
3.7 Construction of projective planes from vector spaces 51
viii Contents
3.8 The Pappus configuration 57
3.9 Projective spaces 60
3.10 Desargues configurations again 63
3.11 Exercises 64
4 Affine spaces 67
4.1 Affine planes 67
4.2 Finite affine planes 69
4.3 Embedding an affine plane in a projective plane 70
4.4 Collineations in affine planes 71
4.5 The Desargues configuration in affine planes 77
4.6 Co ordinatization in affine planes and the Pappus
configuration 79
4.7 Affine spaces 82
4.8 Exercises 85
5 Polar spaces 89
5.1 The definition 89
5.2 Absolute points 91
5.3 Quadrics 94
5.4 Linear subspaces 99
5.5 Irreducibility 103
5.6 Projective spaces inside polar spaces 105
5.7 A history of polar spaces 107
5.8 Exercises 109
6 Generalized quadrangles 112
6.1 Definition and some basic results 112
6.2 All known examples 118
6.3 Some combinatorial properties 120
6.4 Generalized quadrangles with 5 = / = 3 124
6.5 Subquadrangles 127
6.6 Collineations of generalized quadrangles 131
6.7 A brief history of generalized quadrangles 134
6.8 Exercises 135
7 Partial geometries 138
7.1 The definition 138
7.2 A method of constructing proper partial geometries 141
7.3 Strongly regular graphs 142
7.4 Subgeometries 147
7.5 Pasch s axiom 149
7.6 A history of partial geometries 154
7.7 Exercises 155
Contents ix
8 Blocking sets 158
8.1 Definition and examples 158
8.2 Blocking sets in projective planes 159
8.3 Blocking sets in affine planes 163
8.4 Blocking sets in Steiner systems 165
8.5 Blocking sets in generalized quadrangles and partial geometries 167
8.6 Applications of blocking sets 171
8.7 Exercises 173
Bibliography 176
Index of notation 190
Subject index 191
x: blank
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| author | Batten, Lynn M. |
| author_facet | Batten, Lynn M. |
| author_role | aut |
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| classification_rvk | SK 170 SK 380 |
| ctrlnum | (OCoLC)35646618 (DE-599)BVBBV011959510 |
| 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 |
| edition | 2. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:19:12Z |
| institution | BVB |
| isbn | 0521590140 0521599938 9780521599931 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008086916 |
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| physical | XIV, 193 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Batten, Lynn M. Verfasser aut Combinatorics of finite geometries Lynn Margaret Batten 2. ed. Cambridge [u.a.] Cambridge Univ. Press 1997 XIV, 193 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Finite geometries Endliche Geometrie (DE-588)4014650-9 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Endliche Geometrie (DE-588)4014650-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008086916&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Batten, Lynn M. Combinatorics of finite geometries Finite geometries Endliche Geometrie (DE-588)4014650-9 gnd |
| subject_GND | (DE-588)4014650-9 (DE-588)4151278-9 |
| title | Combinatorics of finite geometries |
| title_auth | Combinatorics of finite geometries |
| title_exact_search | Combinatorics of finite geometries |
| title_full | Combinatorics of finite geometries Lynn Margaret Batten |
| title_fullStr | Combinatorics of finite geometries Lynn Margaret Batten |
| title_full_unstemmed | Combinatorics of finite geometries Lynn Margaret Batten |
| title_short | Combinatorics of finite geometries |
| title_sort | combinatorics of finite geometries |
| topic | Finite geometries Endliche Geometrie (DE-588)4014650-9 gnd |
| topic_facet | Finite geometries Endliche Geometrie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008086916&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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