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| Авторизация |
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| Berman G., Fryer K.D. — Introduction to Combinatorics |
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| Предметный указатель |
Multinomial theorem enumeration of labeled trees 16
Multinomial theorem exercises 57
Multinomial theorem positive integer 57
Multiple element sets, example 61
Multiplication principle examples 33
Multiplication principle formulation 33
Multiplication principle number of r-arrangements 38 40
Nodes, trees 13
Non-desarguesian planes, definition 192
Nonempty subsets of set, exercises 8
Nonexistence by exhaustion 134
Nonexistence exercises 139 146
Nonexistence orthogonal latin squares 262
Nonexistence partition of cube 146
Nonexistence tiling rectangle 144
Number of regions of plane, example 10
Number theory, inclusion-exclusion principle 67
Operators definitions 90
Operators exercises 93
Pappus' theorem exercises 195
Pappus' theorem finite fields 194
Pappus' theorem statement 194
Partitions of integers definition 226
Partitions of integers examples 227 228
Partitions of integers exercises 229
Pascal's formula binomial coefficients 48
Pascal's formula derivation 48
Pascal's formula examples 48 49
Pascal's formula exercises 53 241
Pascal's triangle construction 49
Pascal's triangle examples 49 51 117
Pascal's triangle exercises 54 246
Pascal's triangle Fibonacci sequences 245
Permutations definition 35
Permutations derangements 70
Permutations examples 35 36 70 130
Permutations exercises 37 41 72
Permutations product 35
Permutations symbols 34 35
Planes affine 190
Planes Fano 186
Planes non-desarguesian 192
Planes projective 187
Platonic solids discussion 163
Platonic solids exercises 163
Polygons convex 230
Polygons rooted 230
Polyhedra discussion 137
Polyhedra Euler's formula 156
Polyhedra existence 163
Polyhedra maps 155 157
Polyhedra Platonic solids 163
Polynomials difference operator 25
Polynomials evaluating 23
Polynomials exercises 26
Polynomials monic 27
Positive sets attributes 64
Positive sets definition 62
Positive sets derangements 71
Positive sets examples 63 64 66
Positive sets exercises 63 66
Positive sets inclusion-exclusion principle 64
Positive sets number theory 67
Power series, formal 110
Probability discussion 199
Probability distributions definition 212
Probability distributions exercises 213
Probability distributions random walks 233
Probability examples 200—203 235
Probability exercises 77 203 213 238 248
Probability inclusion-exclusion principle 201
Product, permutations 35
Projective configurations characteristic 195
Projective configurations Desargues 193
Projective configurations Pappus 194
Projective planes axioms 187
Projective planes cardinality 188
Projective planes examples 191
Projective planes exercises 189 193
Projective planes existence 188 192
Quadratics exercises 185
Quadratics irreducible 183
Quadratics over finite field 183
r-arrangements, example 40
r-subsets example 48
r-subsets exercises 54
Ramsey problem, chromatic triangles 174
Random walks binomial random walk 234
Random walks difference equation 29
Random walks examples 27 29 49 233 234 236 237
Random walks exercises 30 54 238
Random walks generating functions 29 233
Random walks initial conditions 29
Random walks mean position 29
Random walks one-dimension 27
Random walks probability distributions 233
Random walks recurrence relation 29
Recurrence relations chromatic polynomials 15
Recurrence relations examples 84 88
Recurrence relations exercises 8 84 89
| Recurrence relations grains of wheat caper 7
Recurrence relations iteration 87
Recurrence relations random walks 28
Recurrence relations regions of plane 10
Recurrence relations Stirling numbers 217
Recurrence relations subsets of set 2
Regions of plane example 8
Regions of plane exercises 12
Regions of plane formula 10
Regions of plane induction 11
Regions of plane recurrence relation 10
Regions of plane summation method 12
Relative complement, sets 60
Remainder theorem exercises 26
Remainder theorem formulation 24
Renewal theory, examples 240
Room squares definition 273
Room squares examples 273
Room squares exercises 274
Sample spaces, examples 200
Sequences of plus and minus signs examples 246 247
Sequences of plus and minus signs exercises 248
Sets complement 60
Sets examples 61
Sets exercises 8
Sets inclusion-exclusion principle 60
Sets multiple elements 60
Sets number of nonempty subsets 1
Sets number of nonempty subsets of permutations 35
Sets number of nonempty subsets of subsets 2 53
Sets positive 63
Sets positive rth order 62
Sets relative complement 60
Sperner's lemma exercises 179
Sperner's lemma labeling triangles 175
Steiner triple systems definition 267
Steiner triple systems exercises 267
Stereographic projection, exercise 161
Stirling numbers discussion 217
Stirling numbers exercises 218
Stirling numbers recurrence relation 217
Stirling's formula examples 58
Stirling's formula exercises 59
Stirling's formula factorials 58
Subsets exercises 54
Subsets r-subsets 42
Summation method arithmetic power series 209
Summation method exercises 56 96 211
Summation method general 96
Summation method regions of plane 12
Summation of series, examples 91
Symbols combinations and permutations 34
Symbols number of r-arrangements 38
Symbols permutations 35
Symbols r-subsets 42
Systems of distinct representatives definition 258
Systems of distinct representatives examples 258 259
Systems of distinct representatives exercises 259
Temple of Benares, Tower of Hanoi 6
Tessellations exercises 148
Tessellations existence 147
Tessellations homogeneous 148
Tessellations of plane 147
Tessellations regular 147
Tiling rectangle examples 145
Tiling rectangle exercises 146
Tiling rectangle into congruent squares 143
Tiling rectangle into incongruent squares 143
Tiling rectangle nonexistence 144
Tower of Hanoi exercises 8
Tower of Hanoi induction 5
Tower of Hanoi puzzle formulation 4
Tower of Hanoi Temple of Benares 6
Transformation, difference equation 3
Translation operator, definition 90
Trees branches 13
Trees chromatic polynomials 21 170
Trees definition 13
Trees edges 13
Trees exercises 17 168
Trees existence 22
Trees labeled 13
Trees nodes 13
Trees points 13
Trees vertices 13
Triangulations exercises 179 232
Triangulations generating functions 231
Triangulations polygons 176 230
Trivalent maps, four-color problem 165
Ultimate sets data consistency 206
Ultimate sets definition 205
Ultimate sets discussion 204
Ultimate sets examples 205 206
Ultimate sets exercises 207
Unsolved problems chromatic polynomials 172
Unsolved problems four-color problem 164
Varieties, balanced incomplete block designs 265
Vertices graphs 20
Vertices trees 13
Waiting lines, examples 240
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