The theory of finite linear spaces: combinatorics of points and lines
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge u.a.
Cambridge Univ. Press
1993
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 214 S. graph. Darst. |
| ISBN: | 0521333172 |
Staff View
MARC
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| 245 | 1 | 0 | |a The theory of finite linear spaces |b combinatorics of points and lines |c Lynn Margaret Batten ; Albrecht Beutelspacher |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface page ix
1 The essentials 1
1.1 Definitions and examples 1
1.2 Affine spaces and projective spaces 3
1.3 The connection between affine and projective spaces 10
1.4 The history of finite linear spaces 11
1.5 Some basic results and the Fundamental Theorem 14
1.6 Designs 17
1.7 Another example of a linear space 18
1.8 Exercises 19
1.9 Research problems 20
1.10 References 20
2 Complementation 22
2.1 Aim of the chapter 22
2.2 The details 23
2.3 The pseudo complement theorems 25
2.4 Exercises 31
2.5 Research problems 31
2.6 References 32
3 Line sizes 33
3.1 Introduction 33
3.2 Two consecutive line sizes 34
3.3 Three consecutive line sizes 43
3.4 Two non consecutive line sizes 57
3.5 On the existence of linear spaces with certain line sizes 65
3.6 Exercises 66
v
vi Contents
3.7 Research problems 67
3.8 References 67
4 Semiaffine linear spaces 68
4.1 / Semiaffine linear spaces 68
4.2 {O,l} Semiaffine linear spaces 69
4.3 {0,s,t} Semiaffine linear spaces with non constant point
degree 72
4.4 {s 1,4 Semiaffine linear spaces with constant point degree 80
4.5 {0,1,4 Semiaffine linear spaces with constant point degree 84
4.6 {0,1,2} Semiaffine linear spaces 88
4.7 Exercises 94
4.8 Research problems 95
4.9 References 95
5 Semiaffine linear spaces with large order 96
5.1 Introduction 96
5.2 Embedding linear spaces with constant point degree 104
5.3 Embedding linear spaces with arbitrary point degree 106
5.4 Exercises 118
5.5 Research problems 118
5.6 References 118
6 Linear spaces with few lines 119
6.1 Restricted linear spaces 119
6.2 The combinatorial approach 125
6.3 The algebraic approach 131
6.4 Exercises 134
6.5 Research problems 135
6.6 References 135
7 ^/ Dimensional linear spaces 136
7.1 The definition 136
7.2 Problems in d dimensions 137
7.3 7r Spaces 138
7.4 Local structures 146
7.5 Global conditions 153
7.6 A final embedding theorem 160
7.7 Exercises 164
Contents vii
7.8 Research problems 165
7.9 References 165
8 Group action on linear spaces 167
8.1 Reasons for this chapter and some background 167
8.2 Point and line orbits 168
8.3 Relationships between transitivities 172
8.4 Characterization theorems 176
8.5 Exercises 187
8.6 Research problems 187
8.7 References 187
Appendix 189
Notation index 212
Subject index 213
|
| any_adam_object | 1 |
| author | Batten, Lynn M. Beutelspacher, Albrecht 1950- |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.52 |
| dewey-search | 512/.52 |
| dewey-sort | 3512 252 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
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| indexdate | 2024-07-09T17:33:53Z |
| institution | BVB |
| isbn | 0521333172 |
| language | English |
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| spelling | Batten, Lynn M. Verfasser aut The theory of finite linear spaces combinatorics of points and lines Lynn Margaret Batten ; Albrecht Beutelspacher 1. publ. Cambridge u.a. Cambridge Univ. Press 1993 X, 214 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Action groupe Jussieu Analyse combinatoire Jussieu Espace linéaire fini Jussieu Espaces vectoriels Espaces vectoriels ram Géométrie énumérative Jussieu Table espace linéaire fini Jussieu Vector spaces Dimension n (DE-588)4309313-9 gnd rswk-swf Vektorraum (DE-588)4130622-3 gnd rswk-swf Vektorraum (DE-588)4130622-3 s DE-604 Dimension n (DE-588)4309313-9 s Beutelspacher, Albrecht 1950- Verfasser (DE-588)115416692 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006155205&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Batten, Lynn M. Beutelspacher, Albrecht 1950- The theory of finite linear spaces combinatorics of points and lines Action groupe Jussieu Analyse combinatoire Jussieu Espace linéaire fini Jussieu Espaces vectoriels Espaces vectoriels ram Géométrie énumérative Jussieu Table espace linéaire fini Jussieu Vector spaces Dimension n (DE-588)4309313-9 gnd Vektorraum (DE-588)4130622-3 gnd |
| subject_GND | (DE-588)4309313-9 (DE-588)4130622-3 |
| title | The theory of finite linear spaces combinatorics of points and lines |
| title_auth | The theory of finite linear spaces combinatorics of points and lines |
| title_exact_search | The theory of finite linear spaces combinatorics of points and lines |
| title_full | The theory of finite linear spaces combinatorics of points and lines Lynn Margaret Batten ; Albrecht Beutelspacher |
| title_fullStr | The theory of finite linear spaces combinatorics of points and lines Lynn Margaret Batten ; Albrecht Beutelspacher |
| title_full_unstemmed | The theory of finite linear spaces combinatorics of points and lines Lynn Margaret Batten ; Albrecht Beutelspacher |
| title_short | The theory of finite linear spaces |
| title_sort | the theory of finite linear spaces combinatorics of points and lines |
| title_sub | combinatorics of points and lines |
| topic | Action groupe Jussieu Analyse combinatoire Jussieu Espace linéaire fini Jussieu Espaces vectoriels Espaces vectoriels ram Géométrie énumérative Jussieu Table espace linéaire fini Jussieu Vector spaces Dimension n (DE-588)4309313-9 gnd Vektorraum (DE-588)4130622-3 gnd |
| topic_facet | Action groupe Analyse combinatoire Espace linéaire fini Espaces vectoriels Géométrie énumérative Table espace linéaire fini Vector spaces Dimension n Vektorraum |
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