Berman G., Fryer K.D. — Introduction to Combinatorics :: Электронная библиотека попечительского совета мехмата МГУ

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Berman G., Fryer K.D. — Introduction to Combinatorics

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Название: Introduction to Combinatorics

Авторы: Berman G., Fryer K.D.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1972

Количество страниц: 300

Добавлена в каталог: 20.11.2009

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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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