Pattern recognition on oriented matroids:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
De Gruyter
[2017]
|
| Subjects: | |
| Online Access: | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110530711&searchTitles=true Inhaltsverzeichnis |
| Physical Description: | XI, 219 Seiten Illustrationen |
| ISBN: | 9783110530711 9783110531152 3110530716 |
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MARC
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Record in the Search Index
| _version_ | 1804177900880003072 |
|---|---|
| adam_text | CONTENTS
COMMITTEES FOR PATTERN RECOGNITION: INFEASIBLE SYSTEMS OF LINEAR
INEQUALITIES,
HYPERPLANE ARRANGEMENTS, AND REALIZABLE ORIENTED MATROIDS * 1
INFEASIBLE SYSTEMS OF HOMOGENEOUS STRICT LINEAR INEQUALITIES AND THEIR
COMMITTEES * 1
ARRANGEMENTS OF ORIENTED LINEAR HYPERPLANES AND COMMITTEES OF REGIONS *
REALIZABLE SIMPLE ORIENTED MATROIDS AND TOPE COMMITTEES * 3
1 ORIENTED MATROIDS, THE PATTERN RECOGNITION PROBLEM, AND TOPE
COMMITTEES * 5
1.1 PRELIMINARIES * 5
1.2 PATTERN RECOGNITION ON ORIENTED MATROIDS * 10
1.3 THE EXISTENCE OF A TOPE COMMITTEE: REORIENTATIONS * 17
1.4 GRAPHS RELATED TO TOPE COMMITTEES * 29
1.5 SELECTED MATHEMATICAL CONCEPTS AND TOOLS FOR AN ANALYSIS OF
INFEASIBLE
SYSTEMS OF CONSTRAINTS * 39
NOTES * 50
2 BOOLEAN INTERVALS * 54
2.1 LONG/- AND FT-VECTORS OF FACE SYSTEMS * 55
2.2 FACE SYSTEMS, DISTINGUISHED BASES, AND CHANGE OF BASIS MATRICES * 58
2.3 PARTITIONS OF FACE SYSTEMS INTO BOOLEAN INTERVALS, AND THE
LONG/- AND H-VECTORS. DEHN-SOMMERVILLE TYPE RELATIONS * 62
NOTES * 65
3 DEHN-SOMMERVILLE TYPE RELATIONS * 67
3.1 DEHN-SOMMERVILLE TYPE RELATIONS FOR THE LONG H-VECTORS * 67
3.2 DEHN-SOMMERVILLE TYPE RELATIONS FOR THE LONG/-VECTORS * 70
3.3 THE LONG/-VECTORS OF DS-SYSTEMS, AND INTEGER POINTS IN RATIONAL
CONVEX
POLYTOPES * 72
3.4 THE LONG H-VECTORS OF DS-SYSTEMS, AND INTEGER POINTS IN RATIONAL
CONVEX
POLYTOPES * 78
NOTES * 81
4 FAREY SUBSEQUENCES * 82
4.1 THE FAREY SUBSEQUENCE =F(B(N),
M)
* 83
4.2 THE FAREY SUBSEQUENCE
&{B(2M),
M) * 84
4.3 FAREY DUALITY* 85
NOTES * 87
5 BLOCKING SETS OF SET FAMILIES, AND ABSOLUTE BLOCKING CONSTRUCTIONS IN
POSETS * 88
5.1 BLOCKING ELEMENTS AND COMPLEMENTING ELEMENTS OF SUBPOSETS * 90
5.2 BLOCKING ELEMENTS IN DIRECT PRODUCTS OF POSETS * 93
5.3 THE BLOCKER MAP AND THE COMPLEMENTARY MAP ON ANTICHAINS * 94
5.4 THE LATTICE OF BLOCKERS * 97
5.5 DELETION AND CONTRACTION * 99
5.6 THE BLOCKER, DELETION, CONTRACTION, AND MAPS ON POSETS * 103
5.7 THE BLOCKER, DELETION, CONTRACTION, POWERS OF 2, AND THE SELF-DUAL
CLUTTERS * 106
5.8 THE (X, FC)-BLOCKER MAP* 108
5.9 (X, FC)-DELETION AND (X, ^-CONTRACTION * 112
NOTES * 116
6
COMMITTEES OF SET FAMILIES, AND RELATIVE BLOCKING CONSTRUCTIONS IN
POSETS * 118
6.1 RELATIVELY BLOCKING ELEMENTS OF ANTICHAINS * 119
6.2 ABSOLUTELY BLOCKING ELEMENTS OF ANTICHAINS, AND CONVEX SUBPOSETS *
122
6.3 A CONNECTION BETWEEN ABSOLUTE AND RELATIVE BLOCKING
CONSTRUCTIONS * 127
6.4 THE STRUCTURE OF THE SUBPOSETS OF RELATIVELY BLOCKING ELEMENTS, AND
THEIR
ENUMERATION * 127
6.5 PRINCIPAL ORDER IDEALS AND FAREY SUBSEQUENCES * 130
6.6 RELATIVELY BLOCKING ELEMENTS IN GRADED POSETS, AND FAREY
SUBSEQUENCES * 132
6.7 RELATIVELY BLOCKING ELEMENTS IN THE BOOLEAN LATTICES * 134
6.8
RELATIVELY BLOCKING ELEMENTS
B
WITH THE PROPERTY
B
A
-B
= OE IN THE BOOLEAN
LATTICES OF SUBSETS OF THE SETS {1.......M} * 136
6.9 RELATIVELY BLOCKING ELEMENTS IN THE POSETS ISOMORPHIC TO THE FACE
LATTICES
OF CROSSPOLYTOPES * 138
6.10 RELATIVELY BLOCKING ELEMENTS IN THE PRINCIPAL ORDER IDEALS OF
BINOMIAL
POSETS * 140
NOTES * 142
7 LAYERS OF TOPE COMMITTEES * 143
7.1 LAYERS OF TOPE COMMITTEES, AND RELATIVELY BLOCKING ELEMENTS IN THE
BOOLEAN LATTICE OF TOPE SUBSETS * 143
7.2 LAYERS OF TOPE COMMITTEES, AND RELATIVELY BLOCKING ELEMENTS IN THE
POSET
OF TOPE SUBSETS CONTAINING NO PAIRS OF OPPOSITES * 146
NOTES * 149
8 THREE-TOPE COMMITTEES * 150
8.1 THREE-TOPE COMMITTEES AND ANTI-COMMITTEES * 150
8.2 COMMITTEES OF SIZE 3 WHOSE TOPES HAVE MAXIMAL POSITIVE PARTS * 153
NOTES * 156
9 HALFSPACES, CONVEX SETS, AND TOPE COMMITTEES * 157
9.1 HALFSPACES AND TOPE COMMITTEES * 159
9.2 CONVEX SETS AND TOPE COMMITTEES * 162
9.3 TOPE COMMITTEES CONTAINING NO PAIRS OF OPPOSITES * 164
NOTES * 166
10 TOPE COMMITTEES AND REORIENTATIONS OF ORIENTED MATROIDS * 167
10.1 THE NUMBER OF TOPE COMMITTEES * 168
10.2 THE NUMBER OF TOPE COMMITTEES CONTAINING NO PAIRS OF OPPOSITES *
169
10.3 TOPE COMMITTEES AND REORIENTATIONS OF ORIENTED MATROIDS ON
ONE-ELEMENT
SUBSETS OF THE GROUND SETS * 171
NOTE * 173
11 TOPES AND CRITICAL COMMITTEES * 174
11.1 SYMMETRIC CYCLES IN THE TOPE GRAPH, AND MAXIMAL POSITIVE BASES
O FR (
-----
174
11.2 TOPES AND CRITICAL COMMITTEES * 176
NOTES * 180
12 CRITICAL COMMITTEES AND DISTANCE SIGNALS * 181
12.1 THE DISTANCE SIGNAL OF A SYMMETRIC CYCLE IN THE TOPE GRAPH * 181
12.2 CRITICAL COMMITTEES AND DISTANCE SIGNALS * 184
NOTES * 187
13 SYMMETRIC CYCLES IN THE HYPERCUBE GRAPHS * 188
13.1 DECOMPOSITIONS OF TOPES WITH RESPECT TO SYMMETRIC CYCLES IN THE
TOPE
GRAPHS * 189
13.2 BASIC METRIC PROPERTIES OF DECOMPOSITIONS * 192
13.3 SYMMETRIC CYCLES IN THE HYPERCUBE GRAPHS * 194
NOTES * 197
BIBLIOGRAPHY* 199
LIST OF NOTATION* 209
INDEX* 217
|
| any_adam_object | 1 |
| author | Matveev, Andrey O. |
| author_facet | Matveev, Andrey O. |
| author_role | aut |
| author_sort | Matveev, Andrey O. |
| author_variant | a o m ao aom |
| building | Verbundindex |
| bvnumber | BV044542581 |
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| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| indexdate | 2024-07-10T07:55:26Z |
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| language | English |
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| physical | XI, 219 Seiten Illustrationen |
| publishDate | 2017 |
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| publisher | De Gruyter |
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| spelling | Matveev, Andrey O. Verfasser aut Pattern recognition on oriented matroids Andrey O. Matveev Berlin De Gruyter [2017] XI, 219 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Mustererkennung (DE-588)4040936-3 gnd rswk-swf Orientiertes Matroid (DE-588)4232299-6 gnd rswk-swf Committee methods in pattern recognition, hypercubes, hyperplane arrangements, infeasible systems of linear inequalities, oriented matroids Orientiertes Matroid (DE-588)4232299-6 s Mustererkennung (DE-588)4040936-3 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgab, PDF 978-3-11-053114-5 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-053084-1 X:MVB http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110530711&searchTitles=true DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029941636&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Matveev, Andrey O. Pattern recognition on oriented matroids Mustererkennung (DE-588)4040936-3 gnd Orientiertes Matroid (DE-588)4232299-6 gnd |
| subject_GND | (DE-588)4040936-3 (DE-588)4232299-6 |
| title | Pattern recognition on oriented matroids |
| title_auth | Pattern recognition on oriented matroids |
| title_exact_search | Pattern recognition on oriented matroids |
| title_full | Pattern recognition on oriented matroids Andrey O. Matveev |
| title_fullStr | Pattern recognition on oriented matroids Andrey O. Matveev |
| title_full_unstemmed | Pattern recognition on oriented matroids Andrey O. Matveev |
| title_short | Pattern recognition on oriented matroids |
| title_sort | pattern recognition on oriented matroids |
| topic | Mustererkennung (DE-588)4040936-3 gnd Orientiertes Matroid (DE-588)4232299-6 gnd |
| topic_facet | Mustererkennung Orientiertes Matroid |
| url | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110530711&searchTitles=true http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029941636&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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