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| Lueneburg H. — Tools and fundamental constructions of combinatorial mathematics |
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| Предметный указатель |
Lyndon word 312ff 315 335
map(n,A) 46 109
map(S,T) 109
Mapping, injective 34 358 361 372
Mapping, surjective 35 372
Mappings, number of injective 277
Marriage theorem 373ff 377
Marriage theorem, transfinite version of 371 377
Maximal clement 352
Maximum condition 53
MCh(S) 341
Minimal element 352
Minimum condition 53
Mixed radix representation 55 217
MOD 29 55 70 88
Module, left R- 113
Module, locally cyclic 405
Module, rank of 405
Module, right R- 113
Module, torsion free 405
Moebius function 258 259 301
Moebius inversion 258 300
Monoid 24 26 112
Monomorphism 111 129 136
Multiplication in a Dedekind triple 26
Multiplication in a Dedekind triple, associativity of 26f
Multiplication in a Dedekind triple, cancellation law of 27
Multiplication in a Dedekind triple, commutativity of 26
Multiplication, russian peasant method of 102
Multiplicative 301
n-ary See Operation
n-set 4%
natural order See Order
nchoosek 69
Neutral element 111 123
Normal basis 332
Normal basis theorem 331
Normal subgroup 111
normalizer 244
Open set 365
Operation 109
Operation, binary 26
Operation, constant 110
Operation, miliary 108
Operation, n-ary 30 109
Operation, unary 25
Operator 109
Operator domain 109
Operator group 114 238 277f 299
Operator, n-ary 109
Optimal assignment problem 391
Orbit 238
Ord(g) 142
Ord(S) 341
Order 20 140 338ff 362
Order ideal 142
Order of a group 242
Order of a group element 142
Order, embedding of 347
Order, Gray arithmetik 82
Order, lexical 59 312 350
Order, linear 20 362 372
Order, linear, compatible with succ 30
Order, natural 21 29
Order, natural, compatibility with addition 25
Order, natural, compatibility with multiplication 28
Ordered group 469
Ordered pair 342
Ordered ring 138
P(S) 35 42
p-group 242
p-th root 305ff 309ff 325
par(k) 145
par(X) 85
Parity 72 85 145
Partition key of type (n,k) 191 198 202
Partition key of type (n,k), decoding of 191
Partition key of type (n,k), rank of 199 202
Partition key of type n 171 174 183
Partition key of type n, decoding of 172
Partition key of type n, rank of 177 183
Partition of a set 35 36 166ff
Partition of a set, component of 35
Partition of a set, economical 35 114
Partition of an integer 278
partkey 198 199
partkeynk 199
Pascal's triangle 44
Path 227 237
Permutation 246. See also Inversion
Permutation character 239 241
Permutation group 246
Permutation group, imprimitive 283 298
Permutation group, primitive 283 298
Permutation group, transitive See Transitive
Permutation matrix 290ff 389
Permutation, conjugacy class of 253
Permutation, conjugate of 255f 260
Permutation, cycle decomposition of 253 261f
Permutation, cycle of 252 260 261 281
Permutation, cyclic 255 260
Permutation, cyclic, number of 256
Permutation, even 249
Permutation, inverse of 261f
Permutation, odd 249 280
Permutation, order of 253 254 %lf
Permutation, parity of 253
Permutation, sign of 249 255
Permutations, disjoint 253 254
Pigeon Hole Principle 34 121 143 359 478
Pigeon Hole Principle, dual of 35
Point 38
Polish notation 110
Polynomial ring 432 433
Polynomial, irreducible 333 334 335
Power set 35
Power set, cardinal of 42
powerset 62 64
Pred 15 19
Pred, compatibility with the natural order 21
Presentation 424
Prime 137
Prime field 137f
Principal ideal domain 142
Procedure See Extra appendix
PROGRAM See Extra appendix
Pruefer's code 229
Pseudobasis 401
Q(R) 136
| QUEUE 231
Quotient algebra 117
Quotient set 11 J
Rado's selection principle 370 472
Raising to the power of 41
RANGE 56
Rank 405
Recursion scheme I 7
Recursion scheme II 49
Recursion theorem 22 46.
Recursion versus induction 14f 38 52
Relation 4%4
Relevant part 73 88 89
Representation, binary 58
Representation, decimal 58
Representation, finitary 58 59 73
Representation, mixed radix 55
Representation, q-ary 58
Revdoor 156
Revolving door algorithm 51 145ff 148 345
Revolving door algorithm of integers 125 131
Revolving door algorithm with one 112
Revolving door algorithm, commutative 112 133 134
Revolving door algorithm, ring 112 427
R[G] 428
R[X] 433
SDR 371
Section 339
Semigroup 111 121 416
Semigroup, commutative 125ff
Semigroup, finite 122 143
Semiring 27
sgn 249
Simple group 285
Smith' determinant 259f 335
Spanning forest 229 234 236
Spanning tree 229 250
Sperner's Lemma 343
st(l) 314
Stabilizer 238
STACK 426
Standard factorization 314 316
Steinitz' exchange property 401
Stirling numbers of the first kind 190
Stirling numbers of the second kind 187 189
Stirling numbers, signless 190 261
Subalgebra 13 110
Subcover 367
Subcritical subset 382
Subfield 330 332
Subgroup of Z 142
Subtraction, partial 41
Succ 13 59
Succ, compatibility with the natural order 21
SUM 30
Supp 250
Support 250
Surjective See Mapping
Sylow p-subgioup 24 3
Symmetric difference 41
Symmetric group 122 246ff
Symmetric group, conjugacy classes of 278
Symmetric group, generation of 275
Symmetric group, normal subgroups of 286
Symmetric group, presentation of 424
Symmetric group, restricted 251 286 298
Symmetric group, restricted, group of automorphisms 290
Symmetric polynomial 435 436
Systems of distinct representatives 371
Systems of distinct representatives, lower bound for 380
T(x) 15ff
Tarski-finite 53f
Term 4 08
Term algebra See Free t. a.
Term, degree of 408
Theorem of Alexander 367
Theorem of Birkhoff 390
Theorem of Birkhoff — Witt 458
Theorem of Cauchy 238
Theorem of Egervary and Hall 391
Theorem of Lagrange 239
Theorem of Magnus — Witt 468
Theorem of Schroder and Bernstein 349 363 404
Theorem of Sylow, First 243
Theorem of Sylow, Second 245
Theorem of Sylow, Third 245
Theorem of Tychonoff 369
Theorem of Waring 440 478
Theorem of Wilson 327
Theory of finite differences 189
Time complexity 183 187 237 273 399
Topological product 369
Topological sorting 348
Topological space 365
Topological space, compact 367
topology 365
Topology, base for 366
Topology, discrete 365
Topology, product 369
Topology, subbase for 366
Torsion free 405
Totient function See Euler
Trans See Transpose
Transitive group 244 283 284
Transitive group, abelian group 281
Transitivity 246 280
Transitivity, t-fold 246 280 281 284 298
Transposition 250 280
TREE 228
Tree, spanning 229 250
Trees, number of 230
unary See Operation
Union, reduction to binary 30
Universal associative envelope 453 455
Upper bound 352
Vandermonde determinant 439
Vector space 54 372 404
Vertex 227
Vertex, degree of 228
Vertex, isolated 227
Well-order 20 34
Well-order on a Dedekind triple 20
Word 73 299
Word, decomposition of 315
Word, length of 299 312
Z(G) 242
Zermelo's Lemma 346
Zermelo's Well-Ordering Principle 356 358
Zero divisor 131 133 143 144
Zorn's lemma 353 358 371
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