Finite geometry and combinatorial applications:
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2015
|
Schriftenreihe: | London Mathematical Society student texts
82 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XII, 285 S. graph. Darst. |
ISBN: | 9781107107991 9781107518438 |
Internformat
MARC
LEADER | 00000nam a2200000 cb4500 | ||
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007 | t | ||
008 | 150729s2015 d||| |||| 00||| eng d | ||
010 | |a 015009563 | ||
020 | |a 9781107107991 |9 978-1-107-10799-1 | ||
020 | |a 9781107518438 |9 978-1-107-51843-8 | ||
035 | |a (OCoLC)915382859 | ||
035 | |a (DE-599)BVBBV042723153 | ||
040 | |a DE-604 |b ger |e rakwb | ||
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100 | 1 | |a Ball, Simeon |e Verfasser |4 aut | |
245 | 1 | 0 | |a Finite geometry and combinatorial applications |c Simeon Ball |
264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2015 | |
300 | |a XII, 285 S. |b graph. Darst. | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 1 | |a London Mathematical Society student texts |v 82 | |
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650 | 4 | |a Combinatorial analysis | |
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650 | 0 | 7 | |a Endliche Geometrie |0 (DE-588)4014650-9 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Kombinatorische Analysis |0 (DE-588)4164746-4 |2 gnd |9 rswk-swf |
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830 | 0 | |a London Mathematical Society student texts |v 82 |w (DE-604)BV000841726 |9 82 | |
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999 | |a oai:aleph.bib-bvb.de:BVB01-028154310 |
Datensatz im Suchindex
_version_ | 1804174930211766272 |
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adam_text | ! ix
xi
1
1
6
9
10
15
15
17
19
20
21
25
25
27
30
34
38
40
47
51
51
54
60
Contents
Preface
Notation
Fields
1.1 Rings and fields
1.2 Field automorphisms
1.3 The multiplicative group of a finite field
1.4 Exercises
Vector spaces
2.1 Vector spaces and subspaces
2.2 Linear maps and linear forms
2.3 Determinants
2.4 Quotient spaces
2.5 Exercises
Forms
3.1 o Sesquilinear forms
3.2 Classification of reflexive forms
3.3 Alternating forms
3.4 Hermitian forms
3.5 Symmetric forms
3.6 Quadratic forms
3.7 Exercises
Geometries
4.1 Projective spaces
4.2 Polar spaces
4.3 Quotient geometries
v
61
65
71
74
76
83
93
93
99
105
109
114
117
120
124
124
125
130
132
134
135
137
140
144
147
147
148
151
152
154
155
157
162
164
165
167
172
Contents
4.4 Counting subspaces
4.5 Generalised polygons
4.6 Pliicker coordinates
4.7 Polarities
4.8 Ovoids
4.9 Exercises
Combinatorial applications
5.1 Groups
5.2 Finite analogues of structures in real space
5.3 Codes
5.4 Graphs
5.5 Designs
5.6 Permutation polynomials
5.7 Exercises
The forbidden subgraph problem
6.1 The Erdos-Stone theorem
6.2 Even cycles
6.3 Complete bipartite graphs
6.4 Graphs containing no
6.5 A probabilistic construction of graphs containing no KttS
6.6 Graphs containing no K3,3
6.7 The norm graph
6.8 Graphs containing no K55
6.9 Exercises
MDS codes
7.1 Singleton bound
7.2 Linear MDS codes
7.3 Dual MDS codes
7.4 The MDS conjecture
7.5 Polynomial interpolation
7.6 The A-functions
7.7 Lemma of tangents
7.8 Combining interpolation with the lemma of tangents
7.9 A proof of the MDS conjecture for k p
7.10 More examples of MDS codes of length q + 1
7.11 Classification of linear MDS codes of length 3 + 1 for
k ^ p
7.12 The set of linear forms associated with a linear MDS code
Contents
vii
7.13 Lemma of tangents in the dual space 174
7.14 The algebraic hypersurface associated with a linear
MDS code 177
7.15 Extendability of linear MDS codes 182
7.16 Classification of linear MDS codes of length q + 1 for
k c c^fq 184
7.17 A proof of the MDS conjecture for k c^Jq 189
7.18 Exercises 189
Appendix A Solutions to the exercises 191
A.l Fields 191
A.2 Vector spaces 200
A.3 Forms 206
A. 4 Geometries 213
A.5 Combinatorial, applications 229
Λ.6 Die forbidden subgraph problem 233
A. 7 MDS codes 238
Appendix B Additional proofs 242
B. l Probability 242
B. 2 Fields 243
B .3 Commutative algebra 247
Appendix C Notes and references 263
C. l Fields 263
C.2 Vector spaces 264
C.3 Forms 264
C.4 Geometries 264
C.5 Combinatorial applications 266
C.6 The forbidden subgraph problem 269
C.7 MDS codes 270
C.8 Appendices 271
References 272
Index 282
|
any_adam_object | 1 |
author | Ball, Simeon |
author_facet | Ball, Simeon |
author_role | aut |
author_sort | Ball, Simeon |
author_variant | s b sb |
building | Verbundindex |
bvnumber | BV042723153 |
callnumber-first | Q - Science |
callnumber-label | QA167 |
callnumber-raw | QA167.2 |
callnumber-search | QA167.2 |
callnumber-sort | QA 3167.2 |
callnumber-subject | QA - Mathematics |
classification_rvk | SK 170 SK 380 |
ctrlnum | (OCoLC)915382859 (DE-599)BVBBV042723153 |
dewey-full | 516/.11 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 516 - Geometry |
dewey-raw | 516/.11 |
dewey-search | 516/.11 |
dewey-sort | 3516 211 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
format | Book |
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id | DE-604.BV042723153 |
illustrated | Illustrated |
indexdate | 2024-07-10T07:08:13Z |
institution | BVB |
isbn | 9781107107991 9781107518438 |
language | English |
lccn | 015009563 |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028154310 |
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physical | XII, 285 S. graph. Darst. |
publishDate | 2015 |
publishDateSearch | 2015 |
publishDateSort | 2015 |
publisher | Cambridge Univ. Press |
record_format | marc |
series | London Mathematical Society student texts |
series2 | London Mathematical Society student texts |
spelling | Ball, Simeon Verfasser aut Finite geometry and combinatorial applications Simeon Ball Cambridge Cambridge Univ. Press 2015 XII, 285 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society student texts 82 Finite geometries Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd rswk-swf Endliche Geometrie (DE-588)4014650-9 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Endliche Geometrie (DE-588)4014650-9 s Kombinatorik (DE-588)4031824-2 s Kombinatorische Analysis (DE-588)4164746-4 s DE-604 Erscheint auch als Online-Ausgabe Ball, Simeon Finite geometry and combinatorial applications 978-1-316-25744-9 London Mathematical Society student texts 82 (DE-604)BV000841726 82 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028154310&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Ball, Simeon Finite geometry and combinatorial applications London Mathematical Society student texts Finite geometries Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd Endliche Geometrie (DE-588)4014650-9 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
subject_GND | (DE-588)4031824-2 (DE-588)4014650-9 (DE-588)4164746-4 |
title | Finite geometry and combinatorial applications |
title_auth | Finite geometry and combinatorial applications |
title_exact_search | Finite geometry and combinatorial applications |
title_full | Finite geometry and combinatorial applications Simeon Ball |
title_fullStr | Finite geometry and combinatorial applications Simeon Ball |
title_full_unstemmed | Finite geometry and combinatorial applications Simeon Ball |
title_short | Finite geometry and combinatorial applications |
title_sort | finite geometry and combinatorial applications |
topic | Finite geometries Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd Endliche Geometrie (DE-588)4014650-9 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
topic_facet | Finite geometries Combinatorial analysis Kombinatorik Endliche Geometrie Kombinatorische Analysis |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028154310&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV000841726 |
work_keys_str_mv | AT ballsimeon finitegeometryandcombinatorialapplications |