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Engel K. — Sperner theory
Engel K. — Sperner theory

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Название: Sperner theory

Автор: Engel K.

Аннотация:

Sperner's theorem stimulated the development of a fast-growing theory dealing with external problems on finite sets and, more generally, on finite partially ordered sets. This book presents Sperner theory from a unified point of view, bringing combinatorial techniques together with methods from programming, linear algebra, Lie-algebra representations and eigenvalue methods, probability theory, and enumerative combinatorics.


Язык: en

Рубрика: Математика/Алгебра/Комбинаторика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 429

Добавлена в каталог: 10.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Active      142
Additive      345
Adjacency operator      277
Adjacent      5
Adjoint operator      209
Admissible functions      312
Affine lattice      14
Affine poset      13 152 164 175 261
AK-family      51
All-one-operator      276
Antiblocker      87
Antiblocking type      87
Antichain      5
ARC      5
Asymptotic product theorem      319
Asymptotic Sperner property      326
Asymptotically normal      305
atoms      8
Automorphism      4
AZ-identity      18
B-fainily      93
Backward arc      119
Bandwidth problem      46
Bell number      15 273
Bernstein polynomial      269
Betti sequence      355
Bipartite graph      16
Block      98 337
Boolean lattice      9 175 182 185 195 230 233 237 261 265 279 295
Borsuk's conjecture      69
Boundary      39 77
Breadlh first search      121
Canonically compressed      353
Capacity      117
Capacity constraints      118
Capacity of cut      118
Chain      5
Chain product      9 114 171 175 182 195 230 306 328 332
Characteristic function      6 305
Chebyshev's inequality      268
Chromatic polynomial      272
Clements — Lindstroem theorem      343
CLIQUE      5
Cohen — Macaulay complex      35:5
Cointersecting      7 27 93
Colored Kruskal — Katona Theorem      345
Colored Macaulay Theorem      3552
Coloring      272
Coloring-monotone      275
Commutation property      232
Comparable      4
Complement      376
Complement-free      94 378
Complementary family      8 376
Complete intersection theorem,      54
Component      146
Compressed      41 351
Compressed family      352
Compression      41 333
Connected      146
consecutive      91
Conservation of flow      118
Continuity theorem      305
Continuous random variable      304
Convex combination      84
Convex hull      84
Cost function      121
Cosupport      384
Counting in two different ways      16
Cover      5
Critical path method      140
Cross-unrelated      21
Cubical lattice      10
Cubical poset      10 152 175 185 232
Cut      118
Cutset      19
Cyclic permutation      25
Dag      124
Decreasing function      6
def      124
Degree      4
Degree-property      250
Density function      304
Differential poset      232
Digraph      5
Dilworth's Theorem      116
Dilworth-Greene lattice      248 261
Dimension of a polytope      84
Directed graph      5
Discrete random variable      304
Disjunctive normal form      195
Distribution function      304
Distributive lattice      9 248
Dual poset      6 7
Dual problem      125
Duality theorem      126
Dynamically cointersecting      382
Dynamically intersecting      382
Edge set      4
Edge-isoperimetric problem      40 359
Edge-labelable poset      238
EIP      40
Endpoint      5
entropy      79
Entropy inequality      79
Equilibrium      146
Equipartition      102
Erdoes method      71
Erdoes — Ko — Rado theorem      25
Essential extreme point      88
Essential facet-defining inequality      88
Euclidean space      209
Expected value      140 305
Extreme point      84
Facet      86
Family      5
Fibre      131
Filter      6
Final segment      345
Fisher's Inequality      61
FKG-inequality      267
FKG-poset      270
Flow      117
Flow morphism      157
Flow-augmenting path      119
Forward arc      119
Four-Function Theorem      265
Fractional k-cutset      125
Fractional k-family      132
Fringe vertex      121
full      86
Full rank      211
Full-dimensional      87
Function lattice      10
Function poset      10 152 164 171 175 185 232
Gaussian distribution      305
Generalized profile      352
Generalized rank function      318
Generated filter      6
Generated ideal      6
Generating family      50
Geometric lattice      8 248
Graded poset      7
Graph      4
Graph poset      14 231
Graph space      276
Hall's theorem      180
Hamming graph      358
Hasse diagram      5
Hasse graph      5
Hayman's method      310
Height function      5
Hereditary      86
Homogenous polynomial      64
i-difference representation      373
I-level connected      171
I-log concave      173
I-normal      171
I-representation      368
Ideal      6
Incidence matrix      211 258
Inclusion-unrelated      21
Increasing function      6
Indegree      250
Independence number      276
Independent      5
Independent random variables      305
Induced poset      6
Infimum      6
Initial segment      345
Injective word      114
inner edges      39
Integral capacity      118
Integral flow      118
Integral random variable      307
INTERFACE      197
Intersecting      7 24 27 93 164
interval      5
Inversion poset      248
Involution      213
Isomorphic      4
Isomorphism      4
j-compressed      338
Johnson graph      281
Jordan coefficient      217
Jordan function      217
k-cutset      125
k-cutset property      152
K-family      5 131
k-family problem      131
k-independent family      72
k-LYM inequality      150
k-representation      47
k-saturated      138 182
k-shadow      7
k-Spemer property      8
k-uniform      281
Katona's circle method      26 91
Kernel      211
Key      3
Kneser graph      281
Kniskal — Katona theorem      46
Korshunov Theorem      31
KS-independent      22
L-intersecting      62 296
Labeled vertex      119
Labeling algorithm      121
Lagrange function      146
Lagrange multiplier      146
Lattice      7
Lattice distribution      309
Lattice of noncrossing partitions      198
Lefschetz adjacency operator      277
Lefschetz lowering operator      210
Lefschetz matrix      211
Lefschetz raising operator      210
Length      5
Level      7
Lie-Algebra      246
Lie-property      232
Linear lattice      12 152 175 186 187 233 237 261 279 295
Link      185
Little-submodular      345
Littlewood — Offord problem      189
Locally asymptotically normal      307
Log concave      8
Logarithmically concave      8
Lower shadow      7
Lowering operator      209
Lowering property      260
LYM-inequality      17
Macaulay poset      333
Macaulay Theorem      343
Marginal random vector      79
Matching      5 179
Max-flow min-cut theorem      119
Maximal chain      5
Maximal element      5
Maximal family      5
Maximal flow      118
Maximum family      5
Maximum-edge problem      40 358
Mean      140 305
MEP      40
Minimal cut      118
Minimal element      5
Minimal polynomial      196
Mod-A-family      153
Modular      8
Modular geometric lattice      13 171 175 187 237
Modular lattice      8
Moebius function      255
Moebius inversion      255
Monomial      195
Multilinear polynomial      66
Nested chain order      198
Nested structure of solutions      44
Network      117
New shadow      345
Noncrossing partition      198
Nontrivial intersecting      60
Normal distribution      305
Normal poset      149
Normalized matching property      149
NSS      44
Open problems      27 29 67 93 114 148 162 187 189 193 199 207 246 248 253 261 389
Oracle      31
Orbit      6
Order preserving      6 324
Order-lowering operator      210
Order-raising operator      210
Ordered k-partition      21
Outdegree      250
Outer edges      40
P, q-Spemer family      78
p-group      251
Parameters      7
Parenthesization      183
Parenthesization partition      185
Partially ordered sets      4
Partition lattice      14 199 201 272 314 316 326
Peck poset      229
Peck product theorem      230
Peck quotient theorem      230
Peck rankwise product theorem      231
Permutation invariant      91
Permutohedron lattice      248
Polyhedral complex      355
Polyhedron      85
Polynomial      195
Polytope      84
Posel of submatrices of a matrix      12 232
POSET      4
Poset of colored subsets      344
Poset of ideals      244
Poset of shuffles      197
Poset of subcubes of a cube      12 177 232
Poset of unordered partitions of an integer      207
Poset space      209
Positive semidefinite      277
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