Interval orders and interval graphs: a study of partially ordered sets
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York ; Chichester ; Brisbane ; Toronto ; Singapore
John Wiley & Sons
1985
|
| Series: | Wiley-Interscience series in discrete mathematics
A Wiley-Interscience publication |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xi, 215 Seiten Diagramme |
| ISBN: | 0471812846 |
Staff View
MARC
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| 100 | 1 | |a Fishburn, Peter C. |d 1936-2021 |0 (DE-588)119309890 |4 aut | |
| 245 | 1 | 0 | |a Interval orders and interval graphs |b a study of partially ordered sets |c Peter C. Fishburn |
| 264 | 1 | |a New York ; Chichester ; Brisbane ; Toronto ; Singapore |b John Wiley & Sons |c 1985 | |
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Record in the Search Index
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| adam_text | Contents
1 INTRODUCTION 1
1.1 Binary Relations 1
1.2 Related Sets 2
1.3 Ordered Sets 3
1.4 Linear Extensions 7
1.5 Transitive Reorientations 8
1.6 Intervals and Antichains 11
1.7 Graphs 13
1.8 Preview 16
2 INTERVAL ORDERS 18
2.1 Definitions and Examples 18
2.2 Basic Structures 21
2.3 Magnitudes and Characteristic Matrices 25
2.4 Representation Theorems 28
2.5 Weak Order Extensions 30
3 INTERVAL GRAPHS 35
3.1 Definitions and Examples 35
3.2 Basic Ties to Interval Orders 37
3.3 Linearly Ordered Maximal Cliques 40
3.4 Characterizations of Interval Graphs 46
3.5 Characterizations of Indifference Graphs 50
3.6 Unique Agreement 52
4 BETWEENNESS 57
4.1 Betweenness Relations 57
4.2 Axioms and Preliminary Lemmas 59
4.3 Interval Orders and Graphs 62
ix
x Contents
4.4 Semiorders and Indifference Graphs 70
4.5 Weak and Linear Orders 74
5 DIMENSIONALITY AND OTHER PARAMETERS 76
5.1 Parameters of Posets 76
5.2 Dimension of Posets 79
5.3 Posets of Dimension 2 85
5.4 Dimensions of Semiorders 88
5.5 Dimensions of Interval Orders 92
5.6 Breadth and Depth 95
5.7 Numbers of Related Sets 97
6 EMBEDDED SEMIORDERS AND
INDIFFERENCE GRAPHS 101
6.1 Extremization Problems 101
6.2 Upper Bound and Exact Values 104
6.3 General Bounds 110
6.4 Patterns with Restricted Antichains 116
7 REAL REPRESENTATIONS 122
7.1 The Scott Suppes Theorem 122
7.2 Linear Solution Theory 123
7.3 Probability Intervals 130
7.4 Cantor s Theorem 132
7.5 Closed Interval Representations 134
7.6 General Interval Representations 139
8 BOUNDED INTERVAL ORDERS 144
8.1 Bounded Interval Lengths 144
8.2 Unitary Classes 147
8.3 Length Bounded Interval Orders 148
8.4 Linear Inequalities and Forbidden Picycles 153
8.5 Reducibility Lemmas 157
8.6 Banishing Forbidden Picycles 164
9 NUMBERS OF LENGTHS 170
9.1 Finite Lengths Classes 170
9.2 Two Lengths 173
Contents xi
9.3 Many Lengths 175
9.4 Depth 2 Interval Orders 176
9.5 Discontinuities and Admissible Lengths 179
10 EXTREMIZATION PROBLEMS 186
10.1 Definitions and Conjectures 186
10.2 Basic Theorems 189
10.3 Exact Values 193
10.4 Departures from Linearity 199
10.5 More Conjectures 203
REFERENCES 205
INDEX 211
|
| any_adam_object | 1 |
| author | Fishburn, Peter C. 1936-2021 |
| author_GND | (DE-588)119309890 |
| author_facet | Fishburn, Peter C. 1936-2021 |
| author_role | aut |
| author_sort | Fishburn, Peter C. 1936-2021 |
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| building | Verbundindex |
| bvnumber | BV000299203 |
| callnumber-first | Q - Science |
| callnumber-label | QA171 |
| callnumber-raw | QA171.485 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 140 SK 150 |
| classification_tum | MAT 065f |
| ctrlnum | (OCoLC)11045214 (DE-599)BVBBV000299203 |
| dewey-full | 511.3/2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/2 |
| dewey-search | 511.3/2 |
| dewey-sort | 3511.3 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV000299203 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:11:54Z |
| institution | BVB |
| isbn | 0471812846 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000182483 |
| oclc_num | 11045214 |
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| owner_facet | DE-12 DE-91G DE-BY-TUM DE-384 DE-739 DE-355 DE-BY-UBR DE-29T DE-706 DE-188 DE-83 |
| physical | xi, 215 Seiten Diagramme |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | John Wiley & Sons |
| record_format | marc |
| series2 | Wiley-Interscience series in discrete mathematics A Wiley-Interscience publication |
| spelling | Fishburn, Peter C. 1936-2021 (DE-588)119309890 aut Interval orders and interval graphs a study of partially ordered sets Peter C. Fishburn New York ; Chichester ; Brisbane ; Toronto ; Singapore John Wiley & Sons 1985 xi, 215 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Wiley-Interscience series in discrete mathematics A Wiley-Interscience publication Ensembles partiellement ordonnés Intervallen (wiskunde) gtt Partially ordered sets Halbordnung (DE-588)4158821-6 gnd rswk-swf Ordnung Mathematik (DE-588)4043745-0 gnd rswk-swf Intervallordnung (DE-588)4299296-5 gnd rswk-swf Intervallgraph (DE-588)4162152-9 gnd rswk-swf Intervallordnung (DE-588)4299296-5 s Intervallgraph (DE-588)4162152-9 s DE-604 Halbordnung (DE-588)4158821-6 s Ordnung Mathematik (DE-588)4043745-0 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000182483&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fishburn, Peter C. 1936-2021 Interval orders and interval graphs a study of partially ordered sets Ensembles partiellement ordonnés Intervallen (wiskunde) gtt Partially ordered sets Halbordnung (DE-588)4158821-6 gnd Ordnung Mathematik (DE-588)4043745-0 gnd Intervallordnung (DE-588)4299296-5 gnd Intervallgraph (DE-588)4162152-9 gnd |
| subject_GND | (DE-588)4158821-6 (DE-588)4043745-0 (DE-588)4299296-5 (DE-588)4162152-9 |
| title | Interval orders and interval graphs a study of partially ordered sets |
| title_auth | Interval orders and interval graphs a study of partially ordered sets |
| title_exact_search | Interval orders and interval graphs a study of partially ordered sets |
| title_full | Interval orders and interval graphs a study of partially ordered sets Peter C. Fishburn |
| title_fullStr | Interval orders and interval graphs a study of partially ordered sets Peter C. Fishburn |
| title_full_unstemmed | Interval orders and interval graphs a study of partially ordered sets Peter C. Fishburn |
| title_short | Interval orders and interval graphs |
| title_sort | interval orders and interval graphs a study of partially ordered sets |
| title_sub | a study of partially ordered sets |
| topic | Ensembles partiellement ordonnés Intervallen (wiskunde) gtt Partially ordered sets Halbordnung (DE-588)4158821-6 gnd Ordnung Mathematik (DE-588)4043745-0 gnd Intervallordnung (DE-588)4299296-5 gnd Intervallgraph (DE-588)4162152-9 gnd |
| topic_facet | Ensembles partiellement ordonnés Intervallen (wiskunde) Partially ordered sets Halbordnung Ordnung Mathematik Intervallordnung Intervallgraph |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000182483&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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