Triangulations: structures for algorithms and applications
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Springer
2010
|
| Schriftenreihe: | Algorithms and computation in mathematics
25 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | xiii, 535 Seiten Illustrationen, Diagramme 260 mm x 193 mm |
| ISBN: | 9783642129704 |
Internformat
MARC
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| 245 | 1 | 0 | |a Triangulations |b structures for algorithms and applications |c Jesus A. De Loera, Jörg Rambau, Francisco Santos |
| 264 | 1 | |a Berlin |b Springer |c 2010 | |
| 300 | |a xiii, 535 Seiten |b Illustrationen, Diagramme |c 260 mm x 193 mm | ||
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Datensatz im Suchindex
| _version_ | 1805094603129356288 |
|---|---|
| adam_text |
CONTENTS PREFACE V 1 TRIANGULATIONS IN MATHEMATICS 1 1 .1 COMBINATORICS
AND TRIANGULATIONS 2 1.2 OPTIMIZATION AND TRIANGULATIONS 13 1.3 ALGEBRA
AND TRIANGULATIONS 21 1.4 THE REST OF THIS BOOK 34 EXERCISES 38 2
CONFIGURATIONS, TRIANGULATIONS, SUBDIVISIONS, AND FLIPS 43 2.1 THE
OFFICIAL LANGUAGES IN THE LAND OF TRIANGULATIONS 43 2.1.1 POLYHEDRA AND
CONES 43 2.1.2 POINT CONFIGURATIONS 47 2.1.3 GEOMETRY OF POINT
CONFIGURATIONS 50 2.2 A CLOSER LOOK AT THE DEFINITION OF TRIANGULATION
53 2.2.1 THERE IS ALWAYS A TRIANGULATION 54 2.2.2 A FAMOUS EXAMPLE: THE
DELAUNAY TRIANGULATION 56 2.2.3 REGULAR SUBDIVISIONS AND THEIR STRUCTURE
59 2.3 A BULLET-PROOF DEFINITION OF POLYHEDRAL SUBDIVISIONS 62 2.3.1
POLYHEDRAL SUBDIVISIONS 62 2.3.2 REGULAR SUBDIVISIONS, AGAIN 67 2.4
FLIPS AND THE GRAPH OF TRIANGULATIONS 72 2.4.1 CORANK-ONE CONFIGURATIONS
AND CIRCUITS 72 2.4.2 ALMOST-TRIANGULATIONS AND FLIPS 74 2.5 VECTOR
CONFIGURATIONS AND THEIR TRIANGULATIONS 76 2.5.1 VECTOR CONFIGURATIONS
77 2.5.2 POLYHEDRAL SUBDIVISIONS OF VECTOR CONFIGURATIONS 79 2.5.3
REGULAR SUBDIVISIONS OF VECTOR CONFIGURATIONS 81 2.6 TRIANGULATIONS AS
SIMPLICIAL COMPLEXES 83 2.6.1 SIMPLICIAL COMPLEXES 83 2.6.2 THE /-VECTOR
OF A SIMPLICIAL COMPLEXES 84 2.6.3 LINEAR CONSTRAINTS ON THE /-VECTOR 87
EXERCISES 9 BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/100142624X
DIGITALISIERT DURCH X CONTENTS 3.3.2 THE MAXIMUM POSSIBLE NUMBER OF
TRIANGULATIONS 112 3.3.3 THE MINIMUM POSSIBLE NUMBER OF TRIANGULATIONS
115 3.3.4 THE POSET OF SUBDIVISIONS 116 3.4 FLIPS IN TRIANGULATIONS 119
3.4.1 ALL TRIANGULATIONS OF A POINT SET IN THE PLANE ARE CONNECTED BY
FLIPS 120 3.4.2 EFFECTIVE ENUMERATION OF TRIANGULATIONS 123 3.4.3
FURTHER PROPERTIES OF THE GRAPH OF FLIPS 128 3.5 PSEUDO-TRIANGULATIONS
131 3.6 LIFE IN THREE DIMENSIONS 133 3.6.1 THE NUMBER OF TETRAHEDRA 134
3.6.2 MONOTONE FLIPPING DOES NOT (ALWAYS) WORK 137 3.6.3 THE NUMBER OF
FLIPS 141 3.7 NOTES AND REFERENCES 145 EXERCISES 146 4 A TOOL BOX 149
4.1 COMBINATORICS OF CONFIGURATIONS 149 4.1.1 DEPENDENCES, CIRCUITS, AND
THE INTERSECTION PROPERTY 150 4.1.2 EVALUATIONS, COCIRCUITS, AND THE
UNION PROPERTY 155 4.1.3 GALE TRANSFORMS AND THE DUALITY BETWEEN
CIRCUITS AND COCIRCUITS 160 4.2 MANIPULATING VECTOR CONFIGURATIONS 165
4.2.1 PYRAMIDS AND JOINS 165 4.2.2 PRISMS AND PRODUCTS 167 4.2.3
DELETION 169 4.2.4 CONTRACTION 171 4.2.5 ONE-POINT SUSPENSION 175 4.3
GENERATING POLYHEDRAL SUBDIVISIONS 178 4.3.1 THE PLACING (OR PUSHING)
TRIANGULATION 178 4.3.2 THE PULLING TRIANGULATION 181 4.3.3
LEXICOGRAPHIC TRIANGULATIONS 182 4.3.4 PUSHING AND PULLING REFINEMENTS
183 4.4 TWO EQUIVALENT CHARACTERIZATIONS OF FLIPS 185 4.4.1 FLIPS VIA
CIRCUITS 186 4.4. CONTENTS XI 5.3 STRUCTURE OF THE SECONDARY POLYTOPE
233 5.3.1 EDGES OF THE SECONDARY POLYTOPE 233 5.3.2 MONOTONE PATHS ON
THE SECONDARY POLYTOPE 236 5.3.3 FACETS OF THE SECONDARY POLYTOPE 241
5.4 CHAMBERS 243 5.4.1 THECHAMBERFAN 243 5.4.2 FLIPS IN THE CHAMBER FAN
248 5.5 CONFIGURATIONS WITH FIXED CORANK 257 5.5.1 CONFIGURATIONS WITH D
+ 3 POINTS 257 5.5.2 CONFIGURATIONS WITH D + 4 POINTS 261 5.5.3 LAWRENCE
POLYTOPES AND THE COMPLEXITY OF SECONDARY POLYTOPES 264 EXERCISES 270 6
SOME INTERESTING CONFIGURATIONS 275 6.1 CYCLIC POLYTOPES 275 6.1.1
WARM-UP EXAMPLE: TWO DIMENSIONS 276 6.1.2 COMBINATORIAL PROPERTIES OF
CYCLIC POLYTOPES 277 6.1.3 TRIANGULATIONS AS SECTIONS OF THE CANONICAL
PROJECTION 283 6.1.4 HIGHER STASHEFF-TAMARI POSETS 285 6.1.5 THE
STRUCTURE THEOREM FOR THE FIRST STASHEFF-TAMARI POSET 287 6.1.6 CYCLIC
POLYTOPES HAVE MANY TRIANGULATIONS 290 6.2 PRODUCTS OF TWO SIMPLICES 294
6.2.1 THE PRISM OVER A SIMPLEX 294 6.2.2 THE PRODUCT OF SIMPLICES 299
6.2.3 STAIRCASE TRIANGULATIONS 301 6.2.4 NON-REGULAR TRIANGULATIONS OF
PRODUCTS OF SIMPLICES 304 6.3 CUBES AND THEIR SUBPOLYTOPES 311 6.3.1
SMALL 0/1 NON-REGULAR TRIANGULATIONS 311 6.3.2 TWO SIMPLE WAYS TO
TRIANGULATE ANY CUBE 314 6.3.3 TRIANGULATING HIGH-DIMENSIONAL CUBES.
STATE OF THE ART 316 6.3. _ _ CONTENTS 7.3.3 EXPONENTIAL NUMBER OF
COMPONENTS IN THE GRAPH OF FLIPS 361 7.4 DIMENSION 6: A DISCONNECTED
GRAPH OF TRIANGULATIONS IN GENERAL POSITION 362 7.4.1 THE BUILDING
BLOCK: GALE OCTAGONS 363 7.4.2 SEVENTEEN POINTS IN SPECIAL POSITION 365
7.4.3 A DISCONNECTED SPACE OF TRIANGULATIONS IN GENERAL POSITION 369
EXERCISES 374 ALGORITHMIC ISSUES 377 8.1 TOOLS FOR COMPUTATION 377 8.1.1
CHIROTOPES 377 8.1.2 COMPUTING THE CHIROTOPE 378 8.1.3 COMPUTING CIRCUIT
AND COCIRCUIT SIGNATURES FROM THE CHIROTOPE 383 8.2 VERIFICATION AND
REALIZABILITY 385 8.2.1 CONSTRUCTING REGULAR TRIANGULATIONS IN PRACTICE
386 8.2.2 CHECKING REGULARITY OF A TRIANGULATION 387 8.3 LISTING AND
ENUMERATING TRIANGULATIONS 388 8.3.1 EXPLORING A FLIP-GRAPH COMPONENT
389 8.3.2 ENUMERATION OF ALL TRIANGULATIONS 390 8.3.3 ENUMERATION WITH
SYMMETRY 392 8.3.4 IMPLEMENTATION ISSUES 393 8.4 BOUNDING THE NUMBER OF
TRIANGULATIONS 396 8.5 OPTIMIZATION 398 8.5.1 A LINEAR OPTIMIZATION
APPROACH: THE UNIVERSAL POLYTOPE 400 8.5.2 RELAXATIONS OF THE UNIVERSAL
POLYTOPE AND ITS EDGES 406 8.5.3 EQUIDECOMPOSABLE AND WEAKLY NEIGHBORLY
POLYTOPES 410 8.6 COMPUTATIONAL COMPLEXITY OF TRIANGULATION PROBLEMS 413
8.6.1 A VERY QUICK REVIEW OF COMPLEXITY CLASSES 413 8.6.2 THE HARDNESS
OF THE PLANAR CONSTRAINED TRIANGULATION PROBLEM 415 8.6.3 HARDNESS OF
MINIMUM LENGTH TRIANGULATIONS IN THE PLANE 422 8.6. CONTENTS XI I I 9.4
TRIANGULATIONS AND GROEBNER BASES 478 9.4.1 GROEBNER BASES AND TORIC
IDEALS 479 9.4.2 STURMFELS' CORRESPONDENCE 481 9.5 POLYTOPAL COMPLEXES
AND REGULAR TRIANGULATIONS 488 9.5.1 CENTRAL AND NORMAL FANS AS REGULAR
TRIANGULATIONS 489 9.5.2 SHELLINGS, FLIPS, AND FACE VECTORS 493 9.5.3
POLYTOPALITY VIA REGULAR TRIANGULATIONS 502 EXERCISES 509 BIBLIOGRAPHY
513 INDEX 531 |
| any_adam_object | 1 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.1 |
| dewey-search | 516.1 |
| dewey-sort | 3516.1 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| spelling | De Loera, Jesús A. 1966- Verfasser (DE-588)139768904 aut Triangulations structures for algorithms and applications Jesus A. De Loera, Jörg Rambau, Francisco Santos Berlin Springer 2010 xiii, 535 Seiten Illustrationen, Diagramme 260 mm x 193 mm txt rdacontent n rdamedia nc rdacarrier Algorithms and computation in mathematics 25 Triangulation (DE-588)4186017-2 gnd rswk-swf Informatik (DE-588)4026894-9 gnd rswk-swf Triangulation (DE-588)4186017-2 s Informatik (DE-588)4026894-9 s DE-604 Rambau, Jörg 1966- Verfasser (DE-588)115478515 aut Santos, Francisco 1968- Verfasser (DE-588)1020305630 aut Erscheint auch als Online-Ausgabe, eBook 978-3-642-12971-1 Algorithms and computation in mathematics 25 (DE-604)BV011131286 25 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3452498&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020580661&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | De Loera, Jesús A. 1966- Rambau, Jörg 1966- Santos, Francisco 1968- Triangulations structures for algorithms and applications Algorithms and computation in mathematics Triangulation (DE-588)4186017-2 gnd Informatik (DE-588)4026894-9 gnd |
| subject_GND | (DE-588)4186017-2 (DE-588)4026894-9 |
| title | Triangulations structures for algorithms and applications |
| title_auth | Triangulations structures for algorithms and applications |
| title_exact_search | Triangulations structures for algorithms and applications |
| title_full | Triangulations structures for algorithms and applications Jesus A. De Loera, Jörg Rambau, Francisco Santos |
| title_fullStr | Triangulations structures for algorithms and applications Jesus A. De Loera, Jörg Rambau, Francisco Santos |
| title_full_unstemmed | Triangulations structures for algorithms and applications Jesus A. De Loera, Jörg Rambau, Francisco Santos |
| title_short | Triangulations |
| title_sort | triangulations structures for algorithms and applications |
| title_sub | structures for algorithms and applications |
| topic | Triangulation (DE-588)4186017-2 gnd Informatik (DE-588)4026894-9 gnd |
| topic_facet | Triangulation Informatik |
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