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Matousek J. — Lectures on Discrete Geometry (some chapters)
Matousek J. — Lectures on Discrete Geometry (some chapters)



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Название: Lectures on Discrete Geometry (some chapters)

Автор: Matousek J.

Язык: en

Рубрика: Математика/Геометрия и топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 364

Добавлена в каталог: 19.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Crossing number and forbidden subgraph      62
Crossing number theorem      60 (4.3.1)
Crossing number theorem, application      61 66 73 268
Crossing number theorem, for multigraphs      65 (4.4.2)
Crossing number, odd      62
Crossing number, pairwise      62
Crosspolytope      85
Crosspolytope, almost spherical section      323 329
Crosspolytope, faces      89
Crosspolytope, projection      87 (Ex.2)
Cryptography      36
cube      85
Cube, almost spherical section      320
Cube, faces      90
Cube, Hamming      314
Cube, Hamming, embedding into $\ell_2$      343
Cube, Hamming, measure concentration      315 (14.2.3)
Cubes, union complexity      185
Cup      40
Curve, moment      97 (5.4.1)
Curves, cutting into pseudosegments      73 256 257 257
Curves, incidences      53
Curves, lower envelope      160 179
Curves, single cell      169
Cutting      70
Cutting lemma      70 (4.5.3) 72
Cutting lemma, application      248
Cutting lemma, for circles      75
Cutting lemma, higher-dimensional      154 (6.5.3)
Cutting lemma, lower bound      74
Cutting lemma, proof      74 77 148 156 238
Cutting, on the average      72
Cyclic polytope      97 (5.4.3)
Cyclic polytope, universality      99 (Ex.3)
Cylinders, union complexity      185
d-collapsible simplicial complex      189
D-embedding      332 (15.1.1)
d-intervals, transversal      248 249
d-Leray simplicial complex      189
d-representable simplicial complex      189
d-step conjecture      94
Davenport — Schinzel sequence      160
Davenport — Schinzel sequence, asymptotics      167
Davenport — Schinzel sequence, decomposable      171
Davenport — Schinzel sequence, generalized      168 169
Davenport — Schinzel sequence, realization by curves      162 (Ex.1)
Decomposition problem      156
Decomposition, vertical      75 (Ex.3) 150
Deep below      45
Defining set      152
deg(z) (degree in halving-edge graph)      268
Degree      12
Dehn — Sommerville relations      103
Delaunay triangulation      115 118 120
Delone      see Delaunay
Dense set      43
Density of graph, local      363
Density of hypergraph      214
Dependence, affine      14
det $\Lambda$      33
Determinant and affine dependence      14
Determinant and orientation      208
Determinant and volume      37 (Ex.1)
Determinant of lattice      33
Diagram, Gale      110
Diagram, power      118
Diagram, Voronoi      113
Diagram, Voronoi, abstract      118
Diagram, Voronoi, complexity      117 (5.7.4) 119 184
Diagram, Voronoi, farthest-point      117
Diagram, Voronoi, higher-order      119
Diagram, wiring      130
Diameter and smallest enclosing ball      24 (Ex.5)
Diameter approximation      302
Dilworth's Theorem      278 (Ex.4)
dim($\mathcal F$) (VC-dimension)      227 (10.2.3)
Dimension of polytope      85
Dimension Vapnik-Chervonenkis      see VC-dimension
Dimension, VC-dimension      227 (10.2.3)
Dirac — Motzkin conjecture      56
Dirichlet tessellation      see Voronoi diagram
Dirichlet's theorem      58
Disc, largest empty, computation      119
Discrete subgroup of Rd      33
Discs, transversal      221 249
Discs, union complexity      120 (Ex.9) 185
Distance, Banach — Mazur      323
Distances, distinct      50 64
Distances, distinct, bounds      52
Distances, unit      50
Distances, unit, and incidences      55 (Ex.1)
Distances, unit, for convex position      52
Distances, unit, in $R^3$      52
Distances, unit, in $R^4$      52 55
Distances, unit, in the plane      52
Distances, unit, lower bound      57 (4.2.2)
Distances, unit, on 2-sphere      52
Distances, unit, upper bound      63 (Ex.2)
Distortion      332 (15.1.1)
Distribution, binomial      229
Distribution, normal      314 328
Divisible point      195
Domains of action      117
Dominated (pseudo) metric      358
Double-description method      87
Drawing (of graph)      60
Drawing (of graph), on grid      94
Drawing (of graph), rubber-band      93
Dual polytope      91
Dual set      82 (5.1.3)
Dual set system      234
Dual shatter function      231
Duality of linear programming      223 (10.1.2)
Duality of planar graphs      82
Duality transform      80 (5.1.1) 83
Dvoretzky — Rogers lemma      326 (14.6.2) 329
Dvoretzky's theorem      325 (14.6.1) 329
E(G) (edge set)      12
Edge of an arrangement      51
Edge of arrangement      127
Edge of polytope      88
Edge, halving      252
Edges, pairwise crossing      169
Edges, parallel      169
Edmonds' matching polytope theorem      277
Efficient comparison theorem      286 (12.3.1)
Eigenvalue, second, of graph      347
Eigenvalue, second, of random graph      352
Elekes — Ronyai theorem      54
Elimination, Fourier — Motzkin      87
Ellipsoid method      352
Ellipsoid, almost spherical section      319 (14.4.1)
Ellipsoid, definition      306
Ellipsoid, Lowner — John      307
Ellipsoid, smallest enclosing, computation      307
Embedding into $\ell_1$      351 362 365
Embedding into $\ell_2$      365 (Ex.4)
Embedding into $\ell_2$, algorithm      351
Embedding into $\ell_2$, dimension reduction      334 (15.2.1)
Embedding into $\ell_2$, lower bound      340 343 348 352
Embedding into $\ell_2$, testability      349 (15.5.2)
Embedding into $\ell_2$, upper bound      357 (15.7.1)
Embedding into $\ell_p$      352
Embedding into $\ell_p$, isometric      353 (Ex.4) 353
Embedding into $\ell_\infty$, isometric      354 (15.6.1)
Embedding into $\ell_\infty$, upper bound      355 (15.6.2)
Embedding into arbitrary normed space      341
Embedding of planar-graph metrics      360
Embedding of tree metrics      360 365 365 365
Embedding, distortion and dimension      341
Embedding, distortion and dimension, lower bound      339 (15.3.3)
Embedding, isometric      332
Embedding, volume-respecting      362
Entropy (graph)      291
Envelope of segments      159
Envelope of segments, lower bound      163 (7.2.1)
Envelope of simplices      178
Envelope of triangles      175 (7.5.1) 178
Envelope, lower, of curves      160 179
Envelope, superimposed projections      184
Epsilon-net theorem      228 (10.2.4)
Epsilon-net theorem, application      235 239
Epsilon-net theorem, if and only if form      240
Equivalent polytopes, combinatorially      90 (5.3.4)
Equivalent radius      280
Erdos — Sachs construction      342 (Ex.1)
Erdos — Simonovits theorem      204 (9.2.2)
Erdos — Szekeres lemma      278 (Ex.4)
Erdos — Szekeres Theorem      40 (3.1.3)
Erdos — Szekeres theorem, application      44
Erdos — Szekeres theorem, generalizations      42
Erdos — Szekeres theorem, positive-fraction      211 (9.3.3) 213
Erdos — Szekeres theorem, quantitative bounds      42
Euler function      58
Excess      149
Excl(H) (excluded minor class)      360
Excluded minor, and metric      360
Expander      346
Expander, LPS      341
Exposed point      96 (Ex.8)
Extension of Lipschitz mapping      336
Extension, linear      285
Extremal point      88 96 96
Extreme (in arrangement)      141 (Ex.1)
f-vector      96
f-vector of representable complex      189
Face lattice      90
Face of arrangement      124 128
Face of polytope      88 (5.3.1)
Face, popular      146
Facet of arrangement      124
Facet of polytope      88
Facet, halving      252
Facet, halving, interleaving lemma      262 (11.3.1)
Facet, halving, interleaving lemma, application      263 268 271
Facet, k-facet      251
Factorization, of polynomial      36
Fano plane      51
Farkas lemma      19 19 20
Farthest-point Voronoi diagram      117
Fat objects, union complexity      185
Fat-lattice polytope      106 (Ex.1)
Finite projective plane      51 70
First selection lemma      200 (9.1.1)
First selection lemma, application      241
First selection lemma, proofs      202
Flag      104 127
Flat      14
Flattening lemma      334 (15.2.1)
Flattening lemma, application      340
Flipping (Delaunay triangulation)      118
Forbidden permutation      170
Forbidden short cycles      337
Forbidden subgraph      69
Forbidden subgraph and crossing number      62
Forbidden subhypergraph      204 (9.2.2)
Forbidden submatrix      170
Forbidden subsequence      168
Forest, regular      30 (2.1.2)
Form, linear      37 (Ex.4)
Four-square theorem, Lagrange's      38 (Ex.2.3.1)
Fourier — Motzkin elimination      87
Fraction, approximation by      32 (Ex.4) 32
Fractional Helly theorem      187 (8.1.1)
Fractional Helly theorem for line transversals      247 (10.6.2)
Fractional Helly theorem, application      200 203 245
Fractional packing      222
Fractional transversal      222
Fractional transversal for infinite systems      224
Fractional transversal, bound      244 (10.5.2)
Fractions, approximation by      31 (2.1.3)
Frechet's embedding      354
Freiman's theorem      54
Fueredi — Hajnal conjecture      170
Function, Ackermann      167
Function, convex      12
Function, dual shatter      231
Function, Euler's      58
Function, Lipschitz      316 317
Function, primitive recursive      167
Function, rational, on Cartesian product      55
Function, shatter      228
g(n) (number of distinct distances)      50
g-theorem      104
g-vector      104
Gale diagram      110
Gale transform      106
Gale transform, application      202 266
Gale's criterion      97 (5.4.4)
Gallai-type problem      221
Gallery, art      234 238
Gauss integers      58
Gaussian distribution      328
Gaussian measure      313
Gaussian measure concentration      314 (14.2.2)
General position      15
General position of convex sets      42
Generalized arithmetic progression      54
Generalized Davenport — Schinzel sequence      168 169
Generalized lower bound theorem      104
Generalized lower bound theorem, application      264
Generalized triangle      70 (4.5.3)
Genus, and VC-dimension      239 (Ex.6)
Geometric graph      61 169
Geometry of numbers      29 31
Geometry, real algebraic      129
girth      337
Girth and $\ell_2$-embeddings      352
Goemans — Williamson algorithm for MAXCUT      353 (Ex.5)
Graded lattice      90
Graph      11
Graph drawing      60
Graph drawing, on grid      94
Graph drawing, rubber-band      93
Graph of polytope      89
Graph of polytope, connectivity      89 96
Graph of polytope, number of      135 (Ex.3)
Graph, $K_{r, s$-free      69 72
Graph, bipartite      12
Graph, comparability      278 (Ex.4) 291
Graph, complete      12
Graph, connected      12
Graph, determines a simple polytope      94
Graph, entropy      291
Graph, geometric      61 169
Graph, intersection      135 (Ex.2)
Graph, isomorphism      12
Graph, Moore      341
Graph, perfect      274—279
Graph, random, second eigenvalue      352
Graph, regular      12
Graph, shattering      239 (Ex.5)
Graph, without short cycles      337
Grassmanian      317
Greedy algorithm      225 225
Growth function      see Shatter function
Gruenbaum — Motzkin conjecture      248
h(a) (height in poset)      287
H-polyhedron      84 (5.2.1)
H-polytope      84 (5.2.1)
1 2 3 4 5 6
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