Bjorner A., Vergnas M., Sturmfels B. — Oriented Matroids, Second edition (Encyclopedia of Mathematics and its Applications) :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Bjorner A., Vergnas M., Sturmfels B. — Oriented Matroids, Second edition (Encyclopedia of Mathematics and its Applications)

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Oriented Matroids, Second edition (Encyclopedia of Mathematics and its Applications)

Авторы: Bjorner A., Vergnas M., Sturmfels B.

Аннотация:

This second edition of the first comprehensive, accessible account of the subject is intended for a diverse audience: graduate students who wish to learn the subject, researchers in the various fields of application who want to concentrate on certain theoretical aspects, and specialists who need a thorough reference work. For the second edition, the authors have greatly expanded the bibliography to ensure that it is comprehensive and up-to-date, and have also added an appendix surveying research since the first edition. A list of exercises and open problems ends each chapter.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd

Год издания: 1999

Количество страниц: 557

Добавлена в каталог: 19.04.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\lambda$ -function      373
2-cells      252
2-manifold      488
2-point lines      249 272 273
Acyclic      3 122 123 161 300
Acyclic orientation      2 220
Acyclic reorientation      380 385
Acycloids      156
Adjacent topes      169
Adjacent transpositions      68 267
Adjoint      240 246 263 309 392 472
Affine (oriented) matroid      186 191 220 418—420
Affine arrangement of pseudolines      258
Affine covectors      154
Affine face lattice      186
Affine Gale diagram      389 400 402
Affine hyperplane arrangement      47 186 196 418
Affine plane AG(3,3)      224 273
Affine point configuration      7
Affine pseudoline      257
Affine space      420
Algebraic group      79
ALGORITHMS A, B, DC      430 451—458 467
Allowable sequence      36 43 264 275
Alternating      126
Alternating (oriented) matroid      348 395
Altshuler — Bokowski oriented matroid AB(9)      20 405
Antiparallel extensions      293
Antisymmetric tensors      79
Approximation      145
Arbitrarily prescribable      24
Arbitrarily prescribed slopes      41
Arrangement of halfspaces      10
Arrangement of hemispheres      10
Arrangement of lines      14
Arrangement of pseudocircles      248
Arrangement of pseudohyperplanes      234 245
Arrangement of pseudolines      15 43 252 270 278
Arrangement of pseudospheres      18 227 247
Arrangement of spheres      18
Associated essential arrangement      48
Associated zonotope      55
Atomic lattice      168 216
atoms      159
Augmented face poset      201
Automatic theorem proving      486
Ball      201
Ball axiom      227
Barnette sphere      219 403 410
Barycentric coordinates      209
Basic circuit      115 436
Basic cocircuit      115
Basis      29
Basis axioms      6 123—135
Basis graph      132
Basis monomial ring      91
Basis of an oriented matroid program      437
Basis oracle      433
Basis orientation      6 12 124
Basis polytope      91
Beta invariant      193 195
Big face lattice      161
Big oriented matroid      38 265
Binary matroids      331
Binomial proof      486
Biquadratic final polynomial      360—362. 480
Bistellar flip      484
Bland oriented matroid program      475
Bland's rule      418 452 461 467
Bohne — Dress theorem      63 485
Boundary      201
Bounded complex      186 192 220
Bounded cones      29
Bounded oriented matroid program      424—427
Bounded poset      159
Bounded regions      197 221
Bounded simplicial cone      420
Bounded tableau      440
Bounded topes      195
Boundedness of a linear program      425
Boundedness test      456
Bracket      79
Bracket ring      79 91
Braids      262
Broken circuit complex      223
Bruhat order, strong      74 84 97
Bruhat order, weak      74 268
buildings      76
Caratheodory's theorem      382
Card shuffling      487
Cayley trick      485
Cayley — Menger bideterminant      34
cell      11 48 228
Cell complex of an oriented matroid      177
Cellular interpretation      212
Central hyperplane arrangment      47 92 159
Centrally symmetric      233 236
Chamber      48 76
Chamber systems      76
Characteristic polynomial      76 193
Chirality      33 124
Chirotope      6 21 33 124 126 128 132
Chromatic polynomial      220
Cinderella      486
Circuit axioms      4 103
Circuit orientation      103 113
Circuit signatures      113
Closed cells      201
Closed intervals      160
Closed sides      226
Cobase orientation      119
Cocircuit      12 115
Cocircuit graph      186
Cocircuit incidence matrix      241
Cocover      159
Cohomology      94
Coincide at infinity      473
Coloop      103
Coloring lemmas      119 450
Column selection      456
Combinatorial differential manifolds      78 296 482
Combinatorial Grassmannian      482
Combinatorial isomorphism      41 259
Combinatorially equivalent      48 51
Comodular      136
Complement      93
Complementary slackness      426 449 478
Complex hyperplane arrangement      92
Complex sign vectors      95
Complexification      92 95
composition      102 141 158 292
Computational geometry      29 370 472
Configuration space      481
Conformal composition      141 144 158
Conforms      101
Connected sum      304
Constructible      81 366
Constructions      281
Contractible      215
Contraction      57 108 110 134 146 165341 454
Contravariant elements      324
Convex closure      300
Convex closure operator      152 217
Convex hull      377
Convex polytope      24 162 202 376
Convex realization space      406
Covariant elements      324
Covector      9 11 141 193 233
Covector axioms      159
Cover      159

Coxeter arrangement      66
Coxeter complex      75
Coxeter diagram      68
Coxeter group      69 70 185
Coxeter relations      185 267 268
Criss-cross method      451 461 479
Crossing      40
Crosspoly tope      71
Cryptomorphism      132 144
cube      104 111 116 127 147
Cubical polytope      97
Cubical subdivision      60
Cubical zonotopes      56
CW complexes      202
CYCLE      475
Cyclic polytopes      395
Cycling      452 460
Czasar torus      488
Degenerate cycling      452
Degenerate pivot      443 477
Delaunay polytope      44
Delaunay triangulation      29 31
Deletion      57 133 146 165 341 454
Dihedral group      67
DIMENSION      203
Direct sum      312
Directed edge      430
Directed graph      1
Directed path      475
Direction      28 424
Direction of the pivot step      444
dodecahedron      71
Dual feasibility      443
Dual inconsistent program      446
Dual oriented matroid      4 13 115 437
Dual pairs      118
Dual pivoting property      125
Dual program      421
Dual simplex algorithm      443 453 479
Dual tableau      442
Dual zonotope      63
Duality      45 115 135
Duality theorem      449
EDGE      203 252 429
Edmonds — Fukuda — Mandel oriented matroid EFM(8)      244
Edmonds — Mandel (face) lattice      161 164 377 390
Edmonds — Mandel spheres      218
Efficiency of the simplex method      432
Elementary homotopy      184 185
Elementary interval      182
Elementary vector      44
Enlargement lemma      261 470 476
Entering variable      443
Enumeration      270 305
Enumeration of cells      193
Equivariant homeomorphism      251
Essential arrangement      47 227 245
Euclidean affine (oriented) matroid      472 474
Euclidean intersection property      470
Euclidean oriented matroid      472
Euclidean oriented matroid program      473
Euclidean pseudoarrangements      472
Euler characteristic      215
Euler — Poincare formula      199
Euler's formula      250
Excluded minor characterizations      331 350
Existential theory of the reals, ETR      357 408 486
Exponents      74 77
Extension      255 281
Extension lattice      291 292
Extension properties      472
Extension space conjecture      295 482
Extreme point      111 300
Extreme vertex      123
f-vector      193 199
Face      48 203
Face at infinity      423
Face lattice      51 157 161 164
Face poset      48 201
Facet      48 377
Factorization of strong maps      321 483
Fan      219
Fano plane $F_{7}$       86 224 273
Farkas lemma      122 478
Feasibility      445 446
Feasibility problem      428
Feasibility-preserving pivot      443 459 409
Feasible cocircuit      28 428
Feasible oriented matroid program      424—427 430
Feasible polyhedron      28
Feasible region      423
Feasible tableau      440
Filter      160
Final polynomial      24 350 358
Finite pivot rule      452
Flag vector      193
Flat      103
flipping      300
Fundamental circuit      115
Fundamental cocircuit      115
Gale transform      379 387
Gale's evenness condition      396
gallery      76
Gated set of topes      217
Generalized Baues conjecture      296 414 484
Generalized configurations      236
Generalized Euclidean intersection property      382
Generalized point configurations      5
Geometric complexity      271
Geometric lattice      167
Geometric semilattice      48
Geometric sorting process      372
Global perturbation      295
Goodman's polarity principle      264
Gordan lemma      478
Graded poset      159
Graph distance      169 171
Graph of a program      429
Graph of regions      49
Grassmann variety      78 339
Grassmann — Pluecker relations      6 80 126 341
Grassmann — Pluecker relations, 3-term      138 153 275
Grassmannian simplex      91
Hahn — Banach theorem      382 478
Halfspaces      1—1
Helly's theorem      382
Homotopy      133 184
Homotopy equivalent      215
Homotopy type      215
Hyperplane      47
Hyperplane arrangement      5 46 51
Hyperplane theorem      39 221
icosahedron      71
Incidence matrix      222
Incomparability      103
Induced linear ordering      175
Induced oriented matroid      313
Infeasible oriented matroid program      424 426
Infinite oriented matroids      152
Initial tableau      435
Initialization      456
Inseparability graph      324 345
Inseparable elements      324
Intersection      472
Intersection lattice      228
Intersection poset      48
Intersection properties      203 223 308 470
interval      159
Inversions      97
Inverted geometric lattice      238 240

1 2 3

О проекте