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| Comtet L. — Advanced Combinatorics. The Art of Finite and Infinate Expansions |
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| Предметный указатель |
 -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  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  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
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