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Comtet L. — Advanced Combinatorics. The Art of Finite and Infinate Expansions
Comtet L. — Advanced Combinatorics. The Art of Finite and Infinate Expansions



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Название: Advanced Combinatorics. The Art of Finite and Infinate Expansions

Автор: Comtet L.

Язык: en

Рубрика: Математика/Алгебра/Комбинаторика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 343

Добавлена в каталог: 09.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$T_0$-system      302
'Menages' problem      183 185t 199
'Probleme des menages'      183 185t 199
'Probleme des rencontres'      180 182t
'Rencontre'      180
abbreviations      XI
Abel identity      128
Abelian class      18
Abelian word      18
Acyclic graph      62
Acyclic map      70
Additive functions      189
Adjacent edges      61
adjacent nodes      61
Agglutinating system      301
Aleph, Wronski      208
Algebra, boolean      185
Alike binomial coefficients      293
Alphabet      18 297
Alternating group      233
Alternating inequalities      195
Alternating permutations      259t
Andre      21 258
Animal      226
Antireflexive relation      58
ARC      67
arcsin      167
Arctangent numbers      260t
Arithmetic of binomial coefficients      78
Arithmetical triangle      11 76 291
Arrangement      6 75
Associated Stirling numbers      222t 256t
Atom, supporting      190
Axiomatic set theory      122 123t
Ballot      21 80
Banach matchbox problem      297
banner      219
Bell numbers      210 291 307t
Bell polynomials      133 156 159 162 307t
Bernoulli numbers      48 49t 88 154 220
Bernoulli numbers, generalized      227
Bernoulli polynomials      48 164
Bernoulli random variable      160
Bicolour Ramsey numbers      283 287
Bijection, bijective map      5
Binary Ramsey numbers      287 288t
Binary relation      58
Binary tree      54
Binomial coefficient      9 75 93 293 306t
Binomial coefficients, expansions      75
Binomial coefficients, identities      12 76 127 155
Binomial coefficients, series $(1 + t)^x$      37
Binomial coefficients, sums of inverses of      294
Binomial coefficients, sums of logarithms of      295
Binomial coefficients, sums of powers      90
Binominm formula      12
Birthday problem      297
Block      2 7
Bonferroni inequalities      193 203
Boole, inequalities of      194
Boolean algebra      2 185
Boolean function      185
Bound or dummy variable      30
Bracketing      52 55t 57t 85
Bracketing, commutative      54
Bracketing, generalized (Schroeder)      56 57t
Bruno (formnla of Fab. di)      137
Burnside Formula      149
Canonical disjunctive form      187
Cardinal      2
Carlitz      246
Cartesian product      3
Catalan numbers      53 53t 74 82
Catalan problem      52
Cauchy      39 167 254
Cauchy numbers      293 294t
Cayley formula      63
Cayley representation      262
Central limit theorem      281
Central moments      169
Certain event      190
Characteristic function (in set theory)      5
Characteristic numbers of a random variable      160
Chebyshev polynomials      49 87
Chromatic polynomial      179
Chung-Feller theorem      80
Circles in the plane      73
Circuit in graph      62
Circular permutation      231
Circular word      24
Circulator      109
Circulator, prime      109
CLIQUE      62
Closest integer      110
Cloud      274 276t
Coding, Foata      70
Coefficient of formal series      36
Coincidence of a permutation      180
Collector of pictures      297
Combination      2 7
Combination with repetition      15
Commutative bracketing      54
Complement      2
Complementary graph      62
Complementation      2
Complete product      186
Complete subgraph      62
Component of permutation      261 262t
Composition of functions      40 139 145
Concatenation      18
Concave sequence      268
Conditional partitions of a set      225
Conditional partitions of an integer      98 205
Conditional permutations      256
Configuration      250
Congruences      218 225 229
Conjugate partitions      100
Conjunction      186
Connected component      69
Connected graph      62 166 167t
Connected relation      226
Constant term      38
Convex polygon      74
Convex polyhedron      73 297
Convex sequence      14 114 268
Convolution      44 154 227
Covering      165
cr=circulator      109
cube      250 262
Cumulant      160
Cycle in a graph      62
Cycle indicator polynomial      247 264
Cycle, permutation      231
D'Arcais numbers      159t
Darboux method      277 295
Decomposition into cycles (permutaions)      231
Dedekind      273
Degree of a free monomial      18
Degree of a group of permutations      246
Degree of a node in a graph      61
Delannoy numbers      80
Demorgan formulas      3
Denumerant      108 159'
Denumerant with multi-indexes      124
Derangement      180 182t 199 201 256t
Derangement, random      295
Derivation, formal      41
Derivative, n-th - of a composition of functions      138
Derivative, n-th - of a product of funcions      132
Derivatives of gamma function      173
Derivatives of implicit functions      175t
Determinants      200 203 260
Diagonal of a product      3 58
Diagonal series      42 81
Diagonal steps in a path      80
Diagram of a recurrence relation      12
Diagram, Ferrers      100
Dice, loaded      298
Difference operator      13 83
Difference, set-theoretic      2
Digraph = directed graph      67
Disjunctive canonical form      187
Distance on a tree      62
distribution      8 15 222
Distribution function of a random variable      160
Division      25
Dixon formula      174
Dobinski      210
Dot convention      32
Dummy or bound variable      30
Durfee square identity      119
Edge of a graph      61
Empty products and sums      31 35
Endpoint (in a graph)      61
Enumerator of a set of functions      71
Equal binomial coefficients      93
Equivalence class      59
Equivalence relation      59
Eratosthenes, sieve of      178
Euler circuit      62
Euler function      162 193t 199 203
Euler numbers, polynomials      48 49t 89
Eulerian numbers      51 243t
Eulerian polynomials      199 244 259 292
Even permutation      232
Event      190
Excycle      69
exp t      37
Expectation of a random variable      160
Exponential numbers      210 291 310t
Faa di Bruno, formula of      137
Factorial      6 305t
Factorial moments of a random variable      160
Factorial, falling and rising      83
Factorization, ordered      126
Fall      241
Family, multiplicable, of formal series      39
Family, summable, of formal series      38
Feller      80
Fermat matrices      171
Ferrets diagram      99
Fibonacci numbers      45t 86
Figured number      17
Filter basis      91
Finest partition      220
Finite geometry      303t
Fixed point of a permutation      180 231
Foata coding      70
Folding stamps      267t
Forbidden positions, permutations with      201
Forbidden summands (partitions)      108
Forest      70 90 9It
Formal derivation      41
Formal primitivation      42
Formal series      36
Fraction, integrals of      167
Fraction, rational      87 109 223
Fractionary iterates      144
Fractionary of $e^t - 1$      148t
Frechet inequality      200
Frenet-Serret trihedron      158
Frobenius      249
Fubini formula      228
Fubini, theorem of      32
Function, boolean      185
Function, exponential and ordinary generting      44
Function, generating      43
Function, symmetric      158 214
Functional digraph      191 69
Functions of a finite set      69 79
Functions, composition of      40 138 145
Gamma function, derivatives of      173
Gamma function, stirling expansion      267
Gegenbauer polynomials      50 87
Generalized bracketing      56 57t
Generating function      43
Genocchi numbers      49t
Geometry, finite      91 303t
Gould formula      173
Graph      60
Graph (m -)      264
Graph, complementary      62
Graph, directed or oriented      67
Graphs, labeled and unlabeled      263 264t
Graphs, regular      273 279t
Group of given order      302t
Group of permutations      246
Group, alternating      233
Group, symmetric      231
Gumbel inequalities      201
Hadamard product      85
Halphen      161
HamiltonJan circuit      62
Hankel determinant      87
Harmonic numbers      217
Hasse diagram      67
Height of a tree      52
Hermite formula      150 164
Hermite polynomials      164 50 277
Herschellian type      109
Homogeneous parts      38
Horizontal recurrence relations      209
Hurwitz identity      163
Hurwitz series      85
Idempotent map      91t
Idempotent number      135
Identity permutations      230
Identity, binomial      12 127 76 155
Identity, Jacobi      106 119
Identity, multinomial      28 127
Identity, Rogers — Ramanujan      107
Image      4
Image, inverse      5
Implicit, derivative of an function      175t
In-degree, out-degree      68
Incidence matrix      58 201
Incident edge      61
Inclusion and exclusion principle      176
Independent set      62
Indeterminates in a formal series      36
Indicator polynomial      247 264
Inequalities, linear, in probabilities      190
Inequality Newton      278
Inequality of Bonferroni      193 203
Inequality of Boole      194
Inequality of Frechet      200
Inequality of Gumbel      201
Injection      5
Injectlye map      5
Integral part of x      178
Interchangeable system      179
Inventory      251
Inverse image      5
Inverse map      5
Inverse of a formal series      148 151t
Inverse of some polynomials      164
Inversion formula of Lagrange      148 163
Inversion of a matrix      143 164
Inversions in a permutation      236 240t
Involution      257
1 2 3
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