Combinatorics and partially ordered sets: dimension theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Baltimore u.a.
Johns Hopkins Univ. Pr.
1992
|
| Schriftenreihe: | Johns Hopkins Series in the mathematical sciences
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 307 S. graph. Darst. |
| ISBN: | 0801844258 0801869773 |
Internformat
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| 245 | 1 | 0 | |a Combinatorics and partially ordered sets |b dimension theory |c William T. Trotter |
| 264 | 1 | |a Baltimore u.a. |b Johns Hopkins Univ. Pr. |c 1992 | |
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| 650 | 4 | |a Ensembles partiellement ordonnés | |
| 650 | 4 | |a Combinatorial analysis | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface xi
Chapter 1 Introduction to Dimension
§1. Overview 1
§2. Basic Notation for Partially Ordered Sets 2
§3. Dilworth s Chain Covering Theorem 7
§4. Extensions and Realizers 9
§5. Standard Examples 12
§6. Alternating Cycles 14
§7. Dimension and Width 18
§8. Interpolation and Lifting 21
§9. Removal Theorems and Continuity 21
§10. Lexicographic Sums and Hiraguchi s Inequality 23
§11. Complements of Antichains 26
§12. Reversing Critical Pairs 29
Chapter 2 Crowns, Splits, Stacks, Sums, and Products
§1. Overview 33
§2. Generalized Crowns 34
§3. Cartesian Products 38
§4. Bipartite Posets 46
§5. Splits and Quasi Realizers 48
§6. Stacks and Splits 51
§7. Kelly s Dimension Products 53
§8. Exponents and Distributive Lattices 54
Chapter 3 Characterization Problems for Posets, Lattices, Graphs,
and Eamilies of Sets
§1. Overview 57
§2. Comparability Graphs and Gallai s Theorem 58
§3. The 3 Irreducible Posets—Trotter and Moore s Method 62
§4. Planar Posets and Planar Aographs 66
§5. Planar Lattices 69
§6. The 3 Irreducible Posets—Kelly s Method 77
§7. Stacks and 3 Interval Irreducible Posets 81
vii
viii Contents
§8. Interval Graphs and Interval Orders 86
§9. Linear and Interval Families of Sets 88
§10. Boxes in R 90
§11. Circular Arc Graphs 92
§12. Characterizing Inequalities 93
Chapter 4 Hypergraph Coloring, Computational Complexity, and
Irreducible Posets
§1. Overview 97
§2. Hypergraph Coloring 98
§3. Irreducible Posets 102
§4. Embedding Posets and Kelly s Dimension Products 108
§5. Counting Irreducible Posets 112
Chapter 5 Planar Posets and Trees
§1. Overview 113
§2. Planar Posets with a Zero 114
§3. Planar Posets with Arbitrary Dimension 118
§4. Repeated Splits and Amalgamations 119
§5. Chordal Graphs and Cycle Free Posets 122
Chapter 6 Planar Graphs, Planar Maps, and Convex Polytopes
§1. Overview 127
§2. Schnyder s Dimension Theoretic Test for Planarity 128
§3. Convex Polytopes 132
§4. Normal Families of Paths 135
§5. Constructing Normal Families of Paths 142
§6. Convex Polytopes and Irreducible Posets 149
§7. Planar Multigraphs 151
Chapter 7 Probabilistic Methods in Dimension Theory
§1. Overview 157
§2. Subposets of the Subset Lattice 158
§3. Posets of Bounded Degree 165
§4. The Furedi/Kahn Bounds 166
§5. Random Bipartite Posets 168
§6. Upper Bounds 169
§7. Lower Bounds 171
§8. The Dimension of a Random Labeled Poset 181
§9. Winkler s Model for Random Posets 186
Contents ix
Chapter 8 Interval and Geometric Containment Orders
§1. Overview 189
§2. Interval Orders and Semi orders 190
§3. Dimension Theory for Semi orders and Interval Orders 196
§4. Shift Graphs 197
§5. Ramsey Trails 201
§6. Interval Dimension 202
§7. Containment Orders 204
§8. Degrees of Freedom 209
§9. Circle Orders and Sphere Orders 210
Chapter 9 Greedy Dimension, Back Tracking, and
Depth First Search
§1. Overview 213
§2. The Jump Number Problem 214
§3. Algorithms for Linear Extensions 215
§4. Inequalities for Greedy Dimension 217
§5. Partitions and Constructions 224
§6. Super Greedy Extensions, Back Tracking, and Depth
First Search 235
Chapter 10 Products of Chains of Bounded Length
§1. Overview 247
§2. Embedding Posets in Cubes 247
§3. Matchings in Posets 249
§4. Removal Theorems for ^ Dimension 251
§5. Ramsey Theory for Posets 256
§6. The Maximum Dimension of a Lattice 258
Chapter 11 Large Minimal Realizers
§1. Overview 261
§2. Minimal Realizers and Critical Digraphs 261
§3. Applications of the Rank Reformulation Theorem 268
§4. Generalizing Turan s Theorem 270
Appendix 285
Bibliography 287
Index 301
|
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| isbn | 0801844258 0801869773 |
| language | English |
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| physical | XIV, 307 S. graph. Darst. |
| publishDate | 1992 |
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| publisher | Johns Hopkins Univ. Pr. |
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| series2 | Johns Hopkins Series in the mathematical sciences |
| spelling | Trotter, William T. Verfasser aut Combinatorics and partially ordered sets dimension theory William T. Trotter Baltimore u.a. Johns Hopkins Univ. Pr. 1992 XIV, 307 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Johns Hopkins Series in the mathematical sciences Analise combinatoria larpcal Analyse combinatoire Ensembles partiellement ordonnés Combinatorial analysis Partially ordered sets Halbgeordnete Menge (DE-588)4128951-1 gnd rswk-swf Dimensionstheorie (DE-588)4149935-9 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Kombinatorik (DE-588)4031824-2 s Halbgeordnete Menge (DE-588)4128951-1 s Dimensionstheorie (DE-588)4149935-9 s DE-604 Kombinatorische Analysis (DE-588)4164746-4 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003661581&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Trotter, William T. Combinatorics and partially ordered sets dimension theory Analise combinatoria larpcal Analyse combinatoire Ensembles partiellement ordonnés Combinatorial analysis Partially ordered sets Halbgeordnete Menge (DE-588)4128951-1 gnd Dimensionstheorie (DE-588)4149935-9 gnd Kombinatorik (DE-588)4031824-2 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
| subject_GND | (DE-588)4128951-1 (DE-588)4149935-9 (DE-588)4031824-2 (DE-588)4164746-4 |
| title | Combinatorics and partially ordered sets dimension theory |
| title_auth | Combinatorics and partially ordered sets dimension theory |
| title_exact_search | Combinatorics and partially ordered sets dimension theory |
| title_full | Combinatorics and partially ordered sets dimension theory William T. Trotter |
| title_fullStr | Combinatorics and partially ordered sets dimension theory William T. Trotter |
| title_full_unstemmed | Combinatorics and partially ordered sets dimension theory William T. Trotter |
| title_short | Combinatorics and partially ordered sets |
| title_sort | combinatorics and partially ordered sets dimension theory |
| title_sub | dimension theory |
| topic | Analise combinatoria larpcal Analyse combinatoire Ensembles partiellement ordonnés Combinatorial analysis Partially ordered sets Halbgeordnete Menge (DE-588)4128951-1 gnd Dimensionstheorie (DE-588)4149935-9 gnd Kombinatorik (DE-588)4031824-2 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
| topic_facet | Analise combinatoria Analyse combinatoire Ensembles partiellement ordonnés Combinatorial analysis Partially ordered sets Halbgeordnete Menge Dimensionstheorie Kombinatorik Kombinatorische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003661581&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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