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| Comtet L. — Advanced Combinatorics. The Art of Finite and Infinate Expansions |
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| Предметный указатель |
Isomorphic graphs 263
Iterate, fractionary 144
Iteration polynomials 147t
Jacoobi identity 106 119
Jordan formula 195 200 203
Jordan function 199 203
Juxtaposition, product by 18
Kaplansky 24
Knock-out tournament 200
Kolmogoroff system 302
Labeled graphs 263 264t
Lagrange congruence 218
Lagrange, inversion formula of 148 163
Laguerre polynomials 50
Lah numbers 135 156t
Lalnbert series 48 161
Latin square and rectaugle 183t
Lattice 59
Lattice of partitions of a set 202 220
Lattice of permutations 255
Lattice representation 58
Lattice, free distributive 273
Laurent series 43
Legendre polynomials 50 87 164
Leibniz formula 130
Leibniz numbers 83t
Letter of a word 18
Li Jen-Shu formula 173
Lie derivation 220
Lindeberg 281 297
Linear system 304
Lines in the plane 72
Loaded dice 299
log (1 +t) 37
Logarithmic polynomials 140 156 308t
Logarithmically concave or convex 269
Lower bounds, set of 59
m-composition (partitions) 123
m-selection 4
m-tuple 4
MacMahon X
MacMahon Master Theorem 173
Magic squares 124 125t
MAP 5 70
Map, reciprocal or inverse 5
Map, surjective 5
Maps of a finite set into itself 69
Marriage problem 300
Matchbox problem of Banach 297
Matrix of a permutation 230
Matrix of a relation 58
Matrix, incidence 58 201
Matrix, random 201
Measure 189
Minimal path 20 80 81
minimax 302
Mnlticovering 303t
Model 250 252
Moebius formula 161 202
Moebius function 161
Moment of random variable 160
Money-change problem 108
Monkey typist 297
Monoid, free 18
Monomial, symmetric, function 158
Monotone subsequence 299
Mullinomial coefficient 28 77
Mullinomial identity 28 127
Mullinomial, sums of 126
Mullinomial, sums of inverses of 294
Mulliplicable family 39
Multi-index 36 124
Necklaces 263
Netto X
Newcomb 246 266
Newlon 48 270
Newlon, binomium formula of, formula of Taylor 221
Nmlliplicative function 161
Nmllisection of series 84
Nodes of a graph or digraph 61 67
Nonassociative product 52
octahedron 262
Odd permutations 232
Omino, n- 226
Operator D, derivation 41
Operator E, translation 13
Operator,  difference 13 83
Operator,  220
Operator, P primitivation 52
Orbit 248 231
Order of a focal series 38
Order of a group of pernmtations 246
Order of a permutation 233
Order relation 59 60t
Ordered factorizations 126
Ordered orbits, permutations with 258t
Ordered set 59
Ordinals 122 123t
Out-degree 67
Outstanding elements 258
Overlapping system 303
pair 7
Parity, even or odd 232
Part of a partition 94
Partial relation 58
Partition of an integer 96t 159 292
Partition, random 296
Partitions of a set 30 204
Partitions, lattice of 202 220
Partitions, random, of a set 296
Pascal matrix 143
Pascal triangle 11 76 291
Path in a graph 62
Path, minimal 20 80 81
pcr= prime circulator 109
Pentagonal theorem of Euler 104
Perfect partition of integers 126
Permanent 196
Permutation 7 230
Permutation with forbidden positions 201
Permutation with given order 257t
Permutation with k inversions 236 240t
Permutation with repetitions 27
Permutation, alternating 258 259t
Permutation, circular 231
Permutation, components of 261 262t
Permutation, conditional 233 256
Permutation, cycles of 231
Permutation, generalized 265
Permutation, identity 231
Permutation, parity of 232
Permutation, peak of 261t
Permutation, random 279 295
Permutations, group of 231
Pigeon-hole principle 91
Planes in space 72
Poincare Formula 192
Point, fixed, of a permutation 180 231
Points in the plane 72
Poisson distribution 160
Polya, theorem of 252
Polygon of a permutation 237
Polygon, convex 54 74 299
Polygonal contour 302
Polyhedron, convex 73
Polyhedron, rational points in a 121
Polynomial, indicator, of cycles 247
Positions, permutation with forbidden 201
Potential polynomials 141 156
Powers, sums of 154 168 169
| Pre-image 5 30
Prime circulator 109
Prime numbers 119 178
Primitivation, formal 42
probability 160 190
Probability measure 190
Product set, cartesian 3
Product, empty 35
Profile 125
Projection 3 59
Proper relation 58
q-binomial coefficients 118
Q-identities 103
Quadratic form 300
Quadrinomial coefficients 78t
Ramanujan 107
Ramsey 283 287 288t 298
Random derangements 295
Random formal series 160
Random partition of integers or sets 296
Random permutations 279 295
Random tournament 296
Random variable 160
Random walk 20
Random words 297
Rank of a formula 216
Rational fraction 87 109 223
Rearrangement 265
Reciprocal map 5
Reciprocal of formal series 150 15It
Reciprocal relation 58
Rectangle, latin 182 183t
Reflection principle 22
Reflexive relation 58
Regions, division into 72 73
Regular chains 165
Regular graphs 273 279t
Regular graphs of order 2 276t
Relation 57
Relation, equivalence 59
Relation, incidence 59
Relation, inverse 59
Relation, m-ary 57
Relation, order 59 60t
Renyi 189
Representative, distinct 201 300
Riordan X
Rise in a permutation 240 243t
Rogers — Ramanujan identities 107
Root of a tree 63
Rooted tree 63
Roots of ax = tg x, expansions for - 170t
Roulette 262
Row-independent random variable 280
Run 79
Ryser formula 197
Salie's numbers 86 87t
Sample 190
Schroeder 56 57t 165 223t
Score, score vector 68 123t
Section 59
Separating system 302
Sequences 79 260 265
Sequences, divisions of in] 79
Series random formal 160
Series, diagonal 42 81
Series, formal 36
Sets of n elements (axiomatic) 123t
Shepherds principle 9
Sieve formulas 176
Sieve of Eratosthenes 178
Sign of a permutation 233
Size (of a set) 5
Specification 18 265
Sperner 272 273t 292
Spheres in space 73
Squares in relations 288 291t
Stabilizer 248
Stackings 226
Stamps 124
Stamps, folding strip of- 267t
Standard deviation 160
Standard tableau 125
Steiner, triple-system 303 304t
Step in a minimal path 210
Stirling expansion of gamma function 267
Stirling formula 292
Stirling matrices 146
Stirling numbers 50 135 144 229 271 291 310t
Stirling of the first kind 212
Stirling of the second kind 204
Stirling, associated of the first kind 256t 295
Stirling, associated of the second kind 222t 295
Subgraph 62
Subset 2
Subset, series 40 137
Summable family 38
Summand in a partition of integer 94
Summation formula 153 168 169
Summation set 31
Summation, double 31
Summation, multiple 31
Summation, simple 31 172
Summation, triple 31
Sums of powers of binomial coefficients 90
Surjection 5
Surjective maps 5
Symmetric eulerian numbers 158 214
Symmetric function 158 214
Symmetric group 231
Symmetric monoid 90
Symmetric relation 58
system 3
System of distinct representatives 201 300
System, Sperner 272 273t 292
Tangent numbers 258
Taylor coefficient 130
Taylor series 130
Taylor — Newton formula 221
Terminal edge 62
Terminal node 61
Terms in derivatives of implicit funcions 175t
Terquem problem 79
Topologies on [n] 229t
Total relation 58
Tournament 68
Tournament, knock-out 200
Tournament, random 296
Transitive digraph 66
Transitive relation 58 90
transpositions 231
Transversals in Pascal triangle 76
TREE 62 219
Tree, binary 54
Tree, rooted 63
Triangle, Pascal 11 76
Triangles with integer sides 73
Triangulation 54 74
Trinomial coefficients 78t 163t
Triple Steiner system 303 304t
Type of a partition of a set 205
Type of a permutation 233
Typewriting monkey 297
Unequal summands, partition with 101
Unimodal sequence 269
Unitary series 146
Upperbounds, set of 59
Vandermonde convolution 44 154 227
Variable in formal series 36
Variable, bound or dummy 30
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