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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
Simplicial complex, d-collapsible      189
Simplicial complex, d-Leray      189
Simplicial complex, d-representable      189
Simplicial polytope      91 (5.3.6)
Simplicial sphere      103
Simplification (of level)      76
Single cell in higher dimensions      183 184
Single cell in the plane      169
Site (in Voronoi diagram)      113
Smallest enclosing ball      24 (Ex.5)
Smallest enclosing ellipsoid, computation      307
SO(N)      318
SO(n), measure concentration      314
Sobolev inequalities, logarithmic      315
Sorting with partial information      285—291
Space, $\ell_p$      333
Space, Hilbert      333
Space, metric      331
Space, realization      134
Spanner      343 (Ex.2)
Spanning tree, minimum      120 (Ex.5)
Sphere, measure concentration      310 (14.1.1)
Sphere, simplicial      103
Spherical cap      313
Spherical polytope      121 (Ex.10)
STAB(G) (stable set polytope)      277
Stable set      see Independent set
Stable set polytope      277
Stanley — Wilf conjecture      170
Starshaped      24 (Ex.7)
Steinitz theorem      20 89 93
Steinitz theorem, quantitative      94
Stretchability      131 134
Strong perfect graph conjecture      275
Strong upper bound theorem      104
Subgraph      12
Subgraph, forbidden      69
Subgraph, induced      274
Subgraphs, transversal      249
Subgroup, discrete, of Rd      33
Subhypergraph      203
Subsequence, monotone      278 (Ex.4)
Subset sum problem      36
Subspace, affine      13
Subspace, linear      13
Subspace, random      317
Successive minimum      35
Sum of squares of cell complexities      146 (Ex.1)
Sum, Minkowski      280
Sums and products      56 (Ex.8)
Superimposed projections of lower envelopes      184
Surface patches, algebraic, lower envelope      181
Surface patches, algebraic, single cell      183 (7.7.2)
Surfaces, algebraic, arrangement      128
Surfaces, decomposition problem      156
Sylvester's problem      51
Szemeredi regularity lemma      214 217
Szemeredi — Trotter theorem      49 (4.1.1)
Szemeredi — Trotter theorem, application      56 (Ex.5) 56 56 56 65 67
Szemeredi — Trotter theorem, in the complex plane      52
Szemeredi — Trotter theorem, proof      61 70 72
T(d, r) (Tverberg number)      191
t-almost spherical body      319
Tessellation, Dirichlet      see Voronoi diagram
Theorem, (p,q)      243 (10.5.1)
Theorem, (p,q), for hyperplane transversals      246 (10.6.1)
Theorem, Balinski's      89
Theorem, Borsuk — Ulam, application      26 196
Theorem, Caratheodory's      17 (1.2.3) 19
Theorem, Caratheodory's, application      191 200 300
Theorem, center transversal      27 (1.4.4)
Theorem, centerpoint      26 (1.4.2) 195
Theorem, Clarkson's, on levels      137 (6.3.1)
Theorem, colored Helly      189 (Ex.2)
Theorem, colored Tverberg      194 (8.3.3)
Theorem, colored Tverberg, application      204
Theorem, colored Tverberg, for $r=2$      196
Theorem, colorful Caratheodory      190 (8.2.1)
Theorem, colorful Caratheodory, applicaton      193
Theorem, crossing number      60 (4.3.1)
Theorem, crossing number, application      61 66 73 268
Theorem, crossing number, for multigraphs      65 (4.4.2)
Theorem, Dilworth's      278 (Ex.4)
Theorem, Dirichlet's      58
Theorem, Dvoretzky's      325 (14.6.1) 329
Theorem, Edmonds', matching polytope      277
Theorem, efficient comparison      286 (12.3.1)
Theorem, Elekes — Ronyai      54
Theorem, epsilon-net      228 (10.2.4)
Theorem, epsilon-net, application      235 239
Theorem, epsilon-net, if and only if form      240
Theorem, Erdos — Simonovits      204 (9.2.2)
Theorem, Erdos — Szekeres      40 (3.1.3)
Theorem, Erdos — Szekeres, application      44
Theorem, Erdos — Szekeres, generalizations      42
Theorem, Erdos — Szekeres, positive-fraction      211 (9.3.3) 213
Theorem, Erdos — Szekeres, quantitative bounds      42
Theorem, fractional Helly      187 (8.1.1)
Theorem, fractional Helly, application      200 203 245
Theorem, fractional Helly, for line transversals      247 (10.6.2)
Theorem, g-theorem      104
Theorem, Hadwiger's transversal      248
Theorem, Hahn — Banach      19
Theorem, Hall's, marriage      225
Theorem, ham-sandwich      26 (1.4.3)
Theorem, ham-sandwich, application      209
Theorem, Helly's      21 (1.3.2)
Theorem, Helly's, application      23 (Ex.2) 24 25 83 188 191
Theorem, Helly-type      248 250
Theorem, Helly-type, for containing a ray      24 (Ex.6)
Theorem, Helly-type, for lattice points      279 (Ex.7)
Theorem, Helly-type, for line transversals      84 (Ex.9)
Theorem, Helly-type, for separation      25 (Ex.9)
Theorem, Helly-type, for visibility      25 (Ex.7)
Theorem, Helly-type, for width      23 (Ex.4)
Theorem, Kirchberger's      25 (Ex.9)
Theorem, Koebe's      93
Theorem, Koevari — Sos — Turan      69 (4.5.2)
Theorem, Konig's, edge-covering      225 278
Theorem, Krasnosel'skii's      25 (Ex.7)
Theorem, Kruskal — Hoffman      278 (Ex.6)
Theorem, Lagrange's, four-square      38 (Ex.2.3.1)
Theorem, lattice basis      34 (2.2.2)
Theorem, Lawrence's, representation      133
Theorem, Lipton — Tarjan      62
Theorem, lower bound, generalized      104
Theorem, lower bound, generalized, application      264
Theorem, Milnor — Thom      128 132
Theorem, Minkowski — Hlawka      35
Theorem, Minkowski's      29 (2.1.1)
Theorem, Minkowski's, for general lattices      33 (2.2.1)
Theorem, Minkowski's, second      35
Theorem, Pappus      131
Theorem, Preiman's      54
Theorem, prime number      58
Theorem, Ramsey's      39
Theorem, Ramsey's, application      40 42 43 48 99 346
Theorem, Sard's      16
Theorem, separation      18 (1.2.4)
Theorem, separation, application      19 82 304 350
Theorem, separator      62
Theorem, seven-hole      45 (3.2.2)
Theorem, Steinitz      89 (5.3.3) 93
Theorem, Steinitz's      20
Theorem, Steinitz, quantitative      94
Theorem, Szemeredi — Trotter      49 (4.1.1)
Theorem, Szemeredi — Trotter, application      56 (Ex.5) 56 56 56 65 67
Theorem, Szemeredi — Trotter, in the complex plane      52
Theorem, Szemeredi — Trotter, proof      61 70 72
Theorem, Tverberg's      192 (8.3.1)
Theorem, Tverberg's, application      200
Theorem, Tverberg's, positive-fraction      211
Theorem, Tverberg's, proofs      195
Theorem, two-square      37 (2.3.1)
Theorem, upper bound      100 (5.5.1) 103
Theorem, upper bound, and k-facets      264
Theorem, upper bound, application      117
Theorem, upper bound, continuous analogue      112
Theorem, upper bound, for convex sets      189
Theorem, upper bound, formulation with h-vector      103
Theorem, upper bound, proof      266 (Ex.6)
Theorem, upper bound, strong      104
Theorem, weak epsilon-net      241 (10.4.2)
Theorem, weak epsilon-net, another proof      242 (Ex.1)
Theorem, weak epsilon-net, application      245
Theorem, zone      142 (6.4.1)
Theorem, zone, planar      162 (Ex.5)
Thiessen polygons      117
Topological plane      133
Torus, n-dimensional, measure concentration      314
Total unimodularity      277 278
Trace (of set system)      227
Transform, duality      80 (5.1.1) 83
Transform, Gale      106
Transform, Gale, application      202 266
Transform, medial axis      117
Transversal      84 (Ex.9) 221
Transversal number      221
Transversal number, bound using $\tau^*$      225 231
Transversal of convex sets      243 (10.5.1)
Transversal of d-intervals      248 249
Transversal of discs      221 249
Transversal of subgraphs      249
Transversal same-type      208
Transversal theorem, Hadwiger's      248
Transversal, criterion of existence      209 (9.3.2)
Transversal, fractional      222
Transversal, fractional, bound      244 (10.5.2)
Transversal, fractional, for infinite systems      224
Transversal, hyperplane      246 (10.6.1) 248
Transversal, line      248
Traveling salesman polytope      273
Tree metric      360 364 365 365 365
Tree volume      363
Tree, hierarchically well-separated      364
Tree, spanning, minimum      120 (Ex.5)
Treewidth      249
Triangle, generalized      70 (4.5.3)
Triangles, fat, union complexity      185
Triangles, level in arrangement      176
Triangles, lower envelope      175 (7.5.1) 178
Triangles, VC-dimension      238 (Ex.1)
Triangulation, bottom-vertex      154 156
Triangulation, canonical      see Bottom-vertex triangulation
Triangulation, Delaunay      115 118 120
Triangulation, of arrangement      75 (Ex.2)
Tverberg partition      192
Tverberg point      192
Tverberg's theorem      192 (8.3.1)
Tverberg's theorem, application      200
Tverberg's theorem, colored      194 (8.3.3)
Tverberg's theorem, colored, application      204
Tverberg's theorem, colored, for $r=2$      196
Tverberg's theorem, positive-fraction      211
Tverberg's theorem, proofs      195
Two-square theorem      37 (2.3.1)
Type, order      207 212
U(n) (number of unit distances)      50
Unbounded cells, number of      126 (Ex.2)
Uniform measure      227
Unimodularity, total      277 278
Union, complexity      185
Union, complexity, for discs      120 (Ex.9)
UNION-FIND problem      169
Unit circles, incidences      50 55 57 63 73
Unit circles, Sylvester-like result      52
Unit distances      50
Unit distances and incidences      55 (Ex.1)
Unit distances for convex position      52
Unit distances in $R^3$      52
Unit distances in $R^4$      52 55
Unit distances in the plane      52
Unit distances lower bound      57 (4.2.2)
Unit distances on 2-sphere      52
Unit distances upper bound      63 (Ex.2)
Unit paraboloid      116
Universality of cyclic polytope      99 (Ex.3)
Up-set      286
Upper Bound Theorem      100 (5.5.1) 103
Upper bound theorem, and k-facets      264
Upper bound theorem, application      117
Upper bound theorem, continuous analogue      112
Upper bound theorem, for convex sets      189
Upper bound theorem, formulation with /i-vector      103
Upper bound theorem, proof      266 (Ex.6)
Upper bound theorem, strong      104
V(G) (vertex set)      11
V(x) (visibility region)      235
V-polytope      84 (5.2.1)
Van Kampen-Flores simplicial complex      342
Vapnik — Chervonenkis dimension      see VC-dimension
VC-dimension      227 (10.2.3)
VC-dimension, bounds      232 (10.3.2) 233
VC-dimension, f-vector      96
VC-dimension, f-vector, of representable complex      189
VC-dimension, for halfspaces      232 (10.3.1)
VC-dimension, for triangles      238 (Ex.1)
VC-dimension, g-vector      104
VC-dimension, h-vector      102
VC-dimension, shortest (lattice)      36
VC-dimension, sign (of a face)      124
Veronese mapping      232
Vertex of arrangement      51 127
Vertex of polytope      88
Vertical decomposition      75 (Ex.3) 150
Visibility      234
Visibility, Helly-type theorem      25 (Ex.7)
vol(A)      11
Volume of ball      293
Volume of polytope, lower bound      303
Volume of polytope, upper bound      297 (13.2.1)
Volume of regular simplex      300
Volume, approximation      302
Volume, approximation, hardness      297
Volume, mixed      284
Volume, tree      363
Volume-respecting embedding      362
Voronoi diagram      113
Voronoi diagram, abstract      118
Voronoi diagram, complexity      117 (5.7.4) 119 184
Voronoi diagram, farthest-point      117
Voronoi diagram, higher-order      119
Weak $\varepsilon$-net      248 (10.6.3)
Weak $\varepsilon$-net, for convex sets      240 (10.4.1)
Weak epsilon-net theorem      241 (10.4.2)
Weak epsilon-net theorem, another proof      242 (Ex.1)
Weak epsilon-net theorem, application      245
Weak perfect graph conjecture      275
Weak regularity lemma      214 (9.4.1)
Weak regularity lemma, application      217 (Ex.2) 219
width      23 (Ex.4)
Width, approximation      302 303
Width, bisection      62
Wigner — Seitz zones      117
Wiring diagram      130
x-monotone (curve)      76
X-simplex      199
Zarankiewicz problem      72
Zone in segment arrangement      145
Zone of algebraic variety      145 146
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