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



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Название: Introduction to Combinatorics

Авторы: Berman G., Fryer K.D.

Язык: en

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Affine planes axioms      189 190
Affine planes coordinates      189
Affine planes exercises      189 193
Arithmetic power series discussion      209
Arithmetic power series exercises      211
Arithmetic power series summation method      209
Arrangements circular      39
Arrangements definition      38
Arrangements examples      40
Arrangements exercises      41
Arrangements number of r-arrangements      38
Arrangements with repetitions      39 40
Associative laws, finite fields      181
Averaging method examples      137
Averaging method existence      137
Balanced incomplete block designs blocks      265
Balanced incomplete block designs definition      265
Balanced incomplete block designs examples      267
Balanced incomplete block designs exercises      267
Balanced incomplete block designs Steiner triple system      267
Balanced incomplete block designs varieties      265
Binomial coefficients examples      52
Binomial coefficients exercises      47 54
Binomial coefficients Gaussian      218 221
Binomial coefficients identities      52 53
Binomial coefficients maximum term      51 52
Binomial coefficients Pascal's formula      48
Binomial distribution definition      213
Binomial distribution examples      211
Binomial distribution exercises      213
Binomial identities, exercises      55
Binomial random walk, example      235
Binomial theorem examples      46
Binomial theorem exercises      47
Binomial theorem formulation      45
Binomial theorem maximum term      45
Bipartite graph, definition      259
Birkhoff's theorem chromatic polynomial      18
Birkhoff's theorem proof      20
Birth and death process, examples      241
Blocks, balanced incomplete block designs      265
Boundaries, maps      18
Branches, trees      13
Cayley, counting labeled trees      15
Chessboard, grains of wheat caper      7
Chromatic polynomials Birkhoff's theorem      18
Chromatic polynomials complete graph      97
Chromatic polynomials definition      18
Chromatic polynomials empty graph      97
Chromatic polynomials examples      18 19 68 98 101—105 169
Chromatic polynomials exercises      21 69 106 173
Chromatic polynomials graphs      21 97 168
Chromatic polynomials inclusion-exclusion principle      68
Chromatic polynomials n-gon      170
Chromatic polynomials overlapping graphs      169
Chromatic polynomials properties      171
Chromatic polynomials recurrence relations      100 105
Chromatic polynomials trees      21 170
Chromatic polynomials unsolved problems      172
Chromatic triangles exercises      174
Chromatic triangles Ramsey problem      174
Coloring graphs      167
Coloring maps, exercises      21 167
Coloring planar maps      167
Combinations definition      42
Combinations examples      42 82 119 215
Combinations exercises      43 83 85 216 240
Combinations symbols      34
Combinations with repetitions      82
Combinations without repetitions      42
Commutative laws finite fields      181
Commutative laws Pappus' theorem      194
Complement, sets      60
Computer evaluating polynomials      24
Computer exercises      26 56 59 70 108 229 232 245 256 260 263 275
Conjectures, number of regions of plane      10
Continued fractions, exercises      86
Contradiction method examples      138
Contradiction method exercises      139
Contradiction method existence      138
Convex polyhedron, definition      155
Convex sets convex hull      140
Convex sets convex polygons      230
Convex sets definition      140
Convex sets exercises      142
Convex sets existence      140
Coordinates affine planes      189
Coordinates Desargues' theorem examples      191
Coordinates exercises      193
Coordinates homogeneous      193
Coordinates Pappus' theorem      194
Counting hairs Dirichlet's drawer principle      22
Counting hairs Fibonacci sequences      249
Counting hares discussion      249
Counting hares exercises      249
Counting hares Fibonacci sequence      249
Data consistency examples      206
Data consistency exercises      207
Derangements definition      70
Derangements examples      70
Derangements exercises      72
Derivatives, generating functions      121
Desargues' theorem exercises      195
Desargues' theorem finite fields      194
Desargues' theorem statement      193
Difference equations definition      92
Difference equations examples      92 123 239 240
Difference equations exercises      93 115 120 124 232 241
Difference equations Fibonacci sequence      94 242
Difference equations generating functions      113
Difference equations initial conditions      242
Difference equations nonempty subsets of set      2
Difference equations random walks      29
Difference equations subsets of set      3
Difference methods, operators      90
Difference operator definition      90
Difference operator evaluating polynomials      25
Difference operator examples      90
Difference operator exercises      26
Difference sets definition      268
Difference sets examples      268—270
Difference sets exercises      270
Differential equations examples      122
Differential equations generating functions      122
Dirichlet's drawer principle counting hairs      22
Dirichlet's drawer principle examples      22 136
Dirichlet's drawer principle exercises      23 138
Dirichlet's drawer principle formulation      136
Distribution of objects into boxes examples      214 215
Distribution of objects into boxes exercises      216
Distributive law, finite fields      181
Division ring, Desargues' theorem      194
Edges graphs      20
Edges maps      18
Edges trees      13
Equivalence classes discussion      152
Equivalence classes examples      152 153
Equivalence classes exercises      154
Euler's formula examples      156—159
Euler's formula exercises      160
Euler's formula method of averaging      137
Euler's formula polyhedra      156
Events, examples      200
examples      see “specific entries”
exercises      see “specific entries”
Exhaustion examples      134
Exhaustion exercises      135 185
Exhaustion nonexistence      134
Existence averaging method      137
Existence by construction      129
Existence by exhaustion      133
Existence by trial and error      134
Existence contradiction method      138
Existence convex sets      144
Existence examples      129 133 134
Existence exercises      146 148 167
Existence maps      158 161 165
Existence orthogonal Latin squares      262
Existence projective planes      188 192
Existence regular polyhedra      163
Existence tessellations      147
Existence trees      22
Factorials, Stirling's formula      58
Fano plane examples      186
Fano plane finite      186
Fibonacci algorithm example      253
Fibonacci algorithm exercises      256
Fibonacci algorithm formulation      255
Fibonacci sequences counting hares      249
Fibonacci sequences difference equation      94
Fibonacci sequences examples      118 243 247
Fibonacci sequences exercises      95 120 245 246 249
Fibonacci sequences general term      95
Fibonacci sequences generating functions      243
Fibonacci sequences maximum and minimum      250
Fibonacci sequences representations      242
Fibonacci sequences sequences of plus and minus signs      247
Finite fields associate laws      181
Finite fields cardinality      184
Finite fields characteristic      139 184 195
Finite fields commutative laws      181
Finite fields definition      180 296
Finite fields discussion      180
Finite fields distributive law      181
Finite fields examples      131 138 182 184
Finite fields exercises      132 139 185
Finite planes exercises      189
Finite planes Fano plane      186
Formal power series, examples      3
Four-color problem discussion      164
Four-color problem trivalent maps      165
Gaussian binomial coefficients binomial coefficients      221
Gaussian binomial coefficients definition      218
Gaussian binomial coefficients examples      218—223
Gaussian binomial coefficients exercises      224
Generating functions combinatorial identities      116
Generating functions derivatives      121
Generating functions difference equations      113
Generating functions differential equations      122
Generating functions examples      3 109 111 113 114 116 119 121—124 215 227 228 234
Generating functions exercises      8 112 115 118 120 124 229
Generating functions exponential      110
Generating functions Fibonacci sequences      243
Generating functions random walks      29 233
Generating functions Taylor series      112
Generating functions triangulations      231
Genus, definition      165
Grains of wheat caper exercises      8
Grains of wheat caper induction      7
Grains of wheat caper story      7
Graphs bipartite      259
Graphs chromatic polynomials      21 97 168
Graphs coloring      167
Graphs edges      20
Graphs examples      169
Graphs exercises      168
Graphs labeled      20
Graphs overlapping      169
Graphs planar      167
Graphs vertices      20
Graphs wheel      168
Heawood, coloring theorem      166
Identities binomial coefficients      52
Identities combinatorial      116
Identities generating functions      116
Identity operator, definition      90
Inclusion-exclusion principle applications      67
Inclusion-exclusion principle calculus of sets      60
Inclusion-exclusion principle derangements      71
Inclusion-exclusion principle examples      64 66 83
Inclusion-exclusion principle exercises      66 69 81
Inclusion-exclusion principle linear equations      68 78
Inclusion-exclusion principle number theory      67
Inclusion-exclusion principle positive sets      64
Inclusion-exclusion principle probability      201
Inclusion-exclusion principle symmetric properties      79
Induction exercises      8
Induction number of nonempty subsets of set      2
Induction random walks      28
Induction regions of plane      10
Induction Tower of Hanoi puzzle      5
Initial conditions Fibonacci equation      242
Initial conditions random walks      29
Interval of uncertainty, definition      251
Irreducible, quadratic      183
Iteration examples      171
Iteration exercises      89
Iteration recurrence relations      87
Kirkman schoolgirl problem exercises      264
Kirkman schoolgirl problem formulation      263
Labeled graphs, example      20
Labeled maps, example      20
Labeled trees definition      14
Labeled trees enumeration      13
Labeled trees example      14
Labeled trees exercises      17
Labeling figures, exercises      135
Labeling Sperner's lemma      175
Latin squares definition      130 260
Latin squares examples      131 260
Latin squares exercises      132 263
Latin squares existence      262
Latin squares nonexistence      262
Latin squares orthogonal      131 261
Line at infinity, definition      192
Linear equations bounded solutions      79
Linear equations examples      74—79 215
Linear equations exercises      70 76 80 229
Linear equations inclusion-exclusion principle      68 78
Linear equations nonnegative solutions      74
Linear equations positive solutions      73
Linear equations solutions bounded below      73 76 78
Magic squares construction      272
Magic squares definition      271
Magic squares examples      271
Magic squares exercises      272
Maps boundaries      18
Maps coloring      21
Maps edges      18
Maps Euler's formula      156
Maps examples      129 157 158 159
Maps exercises      132 160 167
Maps existence      158 161
Maps five-color theorem      165
Maps four-color problem      164
Maps Heawood theorem      116
Maps Heawood theorem on sphere      21 155
Maps labeled      20
Maps on surface of genus      166
Maps ordinary      18
Maps planar      164
Maps polyhedral      157
Maps regular      161
Matchings exercises      260
Matchings maximal      259
Maximum and minimum examples      250 252
Maximum and minimum Fibonacci sequences      250
Mean position, random walks      29
Mercator projection, exercise      161
Monic polynomial, definition      27
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