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Электронная библиотека Попечительского совета механико-математического факультета Московского государственного университета
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Bóna M. - Introduction to Enumerative Combinatorics |
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Предметный указатель |
262
Acyclic function 278
Acyclic function, strongly 331
Addition principle 3
Addition Principle, generalized 4
Adjacency matrix 319
Antichain 498
Ascending run 196
ascent 196
Asymptotically equal 40
Automorphism of a graph 262
Ball 412
Bell number 69
BIBD 427
Bijection 22
Binomial coefficient 18
Binomial coefficient for real numbers 126
Binomial theorem 19
Binomial Theorem for real exponents 126
Birkhoff-von Neumann Theorem 477
Block design 400
Burnside lemma 424
Canonical cycle notation 207
Catalan numbers 27 44 151 238 284 290
Cauchy - Binet formula 445
Cayley's formula 266
Chromatic number 340
Chromatic polynomial 295
Code 370
Code, -error correcting 413
Code, instantaneous 372
Code, perfect 416
Code, prefix-free 370
Code, uniquely decipherable 372
composition 62
Composition, weak 60
Compositional formula 170
Conjugacy classes 253
Connected components 257
Convex function 347
Cycle decomposition 206
Cycle, Hamiltonian 395
Cycle, of a graph 259
Cycle, of a permutation 206
Degree sequence 268
Degree sequence, ordered 315
Dependence relation 482
Depth-first search 289
Derangement 219
Desarrangement 203 219
Descent 196
Design 400
Difference of two sets 4
Direct product of two sets 7
Division Principle 15
Division Principle, -to-one function 15
Dur fee- square 106
Erds - Ko - Rado theorem 359
Erds - Rado lemma 363
Erdos - Gallai criterion 116
Eulerian numbers 197
Euler's function 95
Exponential formula 165
Factorial 11
Fano plane 406
Ferrers shapes 72
Ferrers shapes, conjugate 73
Field 409
Finite projective plane 406
Finite projective plane, order of 408
Finite projective plane, over a field 409
Forest 260 274
Forest, rooted 274
Gaussian coefficients 237
Generating functions, ordinary 131
Generating functions, ordinary, doubly exponential 173
Generating functions, ordinary, exponential 140
Graph 256
Graph, -connected 377
Graph, bipartite 302 335
Graph, complete 256
Graph, complete -partite 338
Graph, connected 257
Graph, critically -chromatic 394
Graph, directed 256
Graph, Eulerian 307
Graph, even 309
Graph, minimally connected 258
Graph, regular 352
Graph, undirected 256
Greedy algorithm 392
Group 418
Group, permutation 420
Group, symmetric 419
Hamming code 427
Hamming distance 412
Harmonic numbers 245
Hypergraph 356
Hypergraph, -uniform 358
Hypergraph, balanced 399
Hypergraph, complementary 436
Hypergraph, dual 403
Hypergraph, linked 402
Incidence matrix 403
Inclusion - Exclusion Principle 90
Incomparable edges 364
Independence number 394
Induction, strong 513
Induction, weak 511
Infinite product 153
| inversion 222
Involution 218
Isomorphism classes 262
Isomorphism of graphs 261
Isomorphism of hypergraphs 403
Jensen's Inequality 348
Kraft's inequality 370
Laplacian 312
Latin square 493
Log-concave sequence 443
Log-concave sequence, strongly 460
Log-convex sequence 458
Loop 256
Macmillan's theorem 373
Magic cube 490
Magic cube, irreducible 492
Magic labeling 495
Magic square 470
Magic square, double 496
Magic square, symmetric 495
Major index 228
Matching 333
Matching, in bipartite graphs 460 478
Matching, perfect 333
Matrix-tree theorem 311
Matroid 393
Motzkin number 189
Multinomial coefficient 33
Multinomial theorem 56
Multiset 59
Narayana numbers 287 458
NE lattice path 25 451
Orbit 420
Ordered pair 7
Parking function 280
Parking function, -shortened 315
Parking function, prime 315
Partition of a set 63
Partition of an integer 70
Partition, conjugate 73
Pascal triangle 29
Path 256
Path, Hamiltonian 395
Pentagonal number theorem 74
Permutation 12
Permutation matrix 224
Permutation with repetition 32
Permutation, conjugate 253
Permutation, even 223
Permutation, odd 223
Permutation, order of 235
Permutation, pattern avoiding 238
Philip Hall's theorem 460 478
Pigeonhole Principle 35
Power series 125
Power series formal 127
Product Formula, ex 157
Product Formula, ord. gen. functions 145
Product Principle 6
Product Principle, generalized 7
Products of permutations 204
Proof, bijective 23
Proof, by contradiction 35
Proof, by induction 7 512 513
Proper coloring 293
Property 367
Quasi-polynomial 493
Ramsey numbers 378
Real zeros property 453
Reflection principle 440
Rolle's Theorem 454
Schlmilch's formula 232
Schrder number 189
Semifactorial 138
Small Fermat theorem 430
Sperner's Theorem 365
Sphere 412
Stabilizer 422
Standard Young tableau 25 103
Star 354
Stirling number of the first kind 211
Stirling number of the second kind 65
Stirling number, explicit form for 93 232
Stirling number, signless, of the first kind 207
Stirling's formula 40
Subgraph 337
Subgraph, induced 337
Subgroup 420
Subtraction Principle 4
Successive ranks 106
Sunflower 363
Taylor series 126
Taylor series, -design 427
tetrahedron 238
Tournament 394
Transition lemma 214
Transposition 226
Transposition, adjacent 254
TREE 259
Tree, binary plane 289 290
Tree, doubly rooted 266
Tree, monotone labeled 316
Tree, rooted plane 284
Turn's theorem 340
Twelvefold Way 99
Type of a permutation 212
Unimodal sequence 365 440
Walk 256
Walk, Eulerian 308
Weak direct product 376
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