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| Bona M. — Combinatorics of Permutations |
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| Предметный указатель |
Algebraic power series 181
Alternating group 78
Andre permutation 35
Anti-automorphism 267
ascent 3
Asymptotically equal 139
Asymptotically equal, logaritmically 139
Average number of cycles 90
Avoiding a pattern 129
Balanced tableau 259
Basis 177
Bayes's theorem 223
Bell numbers 169
Bessel function 39
Bruhat order 255
Bruhat order, weak 258
Canonical cycle notation 75
Catalan numbers 133
Cauchy's convolution formula 9
Chain complex 267
Change of directions 24
Chebysev's inequality 235
Chromatic number 38
Chromatic polynomial 38
Class of permutations 138
Class of permutations closed 176
Class of permutations strong 184
Class of permutations weak 150
Column insertion 251
Comparability graph 277
Complement of a permutation 130
Complementary board 225
Complementing method 186
Compositional formula 119
Conditional probability 222
Conjugacy class 81
Convex hull 275
Convolution 180
Corner, inner 217
Corner, outer 225
Critical pair 141
Crossing 207 272
Cycle index 110
Cycle index, augmented 110
Cycles of a permutation 74
D-finite series 178
Darroch's theorem 89
Decreasing binary tree 34
Denert statistic 66
Denert table 327
Deque 300
Deque general 300
Deque input restricted 303
Deque output restricted 303
Derangement 106
Desarrangement 118
Descent of a permutation 3
Descent of a Standard Young T. 240
Determinant 55
Dimension of a poset 273
Euler numbers 319
Euler — Mahonian statistic 67
Euler's formula 51
Euler's formula, real zeros property of 23
Eulerian numbers 5
Eulerian numbers, explicit formula for 8
Eulerian numbers, log-cocavity of 18
Eulerian polynomials 14
Excedance 24
Excedance weak 32 98
Expectation 229
Expectation, linearity of 231
Exponential formula 103
Exponential formula, permutation version 104
Ferrer's shape 47
Fibonacci number 342
Fibonacci number, generalized 169
Fine number 171
Frequency sequence 198
Frobenius formula 221
Fueredi — Hajnal conjecture 159
Fundamental subsequence 185
Gaussian coefficient 58
Gaussian polynomial 59
Geometric form 196
Graded poset 255
Greene — Fomin — Kleitman th. 277
Hamiltonian cycle 240 242
Hook 215
Hook walk 217
Hook walk, special complementary 225
Hooklength formula 216
Indicator random variable 231
Infinite antichain 266
Inserting an entry 185
Internal zero 199
inversion 43
Inversion of a perm of a multiset 57
Inversion of a permutation 43
Inversion of a tree 65
Inversion table 326
Involution 105
Involution fixed-point free 105
Involution vexillary 165
Lagrange inversion formula 114
Lattice 273
Lattice complemented 273
Left-to-right maximum 98
Left-to-right minimum 130
Leg length 259
Levy's theorem 95
Lexicographic order 281
Log-concave sequence 18
Logarithmic asymptotics 140
Longest increasing subsequence 236
Major index 52
Major index of a perm of a multiset 62
Major index of a permutation 52
Major index of a Standard Young T. 242
Maps rooted bicubic 157
Maps, nonseparable rooted 289
Markov's inequality 232
Mean 229
Menger's Theorem 276
Moebius function 244
Motzkin numbers 279 340
Motzkin paths 206
Narayana numbers 171
Normalization 151
Northeastern lattice path 17 170 271
Outer rim 49
P-recursive sequence 33 175
| Packing density 192
Parking function 68
Partition noncrossing 272
Partition of a set 11
Partition of an integer 47
Pattern avoidance 129
Pattern avoidance for graphs 160
Pattern avoidance for matrices 159
Pattern avoidance for perm of multisets 168
Pattern avoidance for permutations 129
Patterns distinct 207
Patterns generalized 169
Patterns layered 193
Patterns length four 135
Patterns monotone 133
Patterns of length three 130
Peak 24
Pentagonal number 48
Perfect matching 56
Permutahedron 272
Permutation 1
Permutation 2-ordered 64
Permutation alternating 32
Permutation Andre 35
Permutation conjugate 80
Permutation cyclic 82
Permutation decomposable 146
Permutation even 77
Permutation fixed-point free 107
Permutation gd-obtainable 300
Permutation gd-sortable 303
Permutation half-ascending 27
Permutation indecomposable 145
Permutation ir-sortable 303
Permutation j-half-ascending 27
Permutation Mahonian 53
Permutation matrix 75
Permutation min-wise independent 241
Permutation obtainable 299
Permutation odd 77
Permutation of a multiset 57
Permutation or-sortable 305
Permutation orderly 140
Permutation partial 56
Permutation q-optimal 192
Permutation random 213
Permutation reverse alternating 319
Permutation separable 308
Permutation series sortable 308
Permutation skew-merged 168
Permutation sorted 307
Permutation stack sortable 286
Permutation statistic 24
Permutation statistic Euler — Mahonian 68
Permutation statistic Eulerian 24
Permutation t-stack sortable 287
Permutation two-stack sortable 287
Permutation, cycle notation of 74
Permutation, two-line notation of 73
Pop-stack 308
Pop-stack in parallel 312
Postorder 150 292
Product formula 101
Projection, horizontal 219
Projection, vertical 219
q-binomial coefficient 58
q-log-concavity 68
q-multinomial coefficient 58
q-unimodality 69
QUEUE 300
r-derangement 121
r-Eulerian numbers 32
r-major index 64
Random variable 229
Rank generating function 275
Rank symmetric poset 264
Real zeros only 21
Reduced decomposition 259
Replace an entry by a pattern 167
Reverse of a permutation 130
Riffle shuffle 241
Right-to-left maximum 138
Risk algorithm 245
Robinson — Schensted — Knuth alg. 245
Row insertion 251
runs 5
Runs, alternating 24
Runs, ascending 5
Runs, tight ascending 38
Schloemilch's formula 92 113
Schroeder numbers 338
Secant numbers 319
Self-dual poset 264
Shape-Wilf equivalence 173
SIGN 328
Simplicial complex 36 267
Square root of a perm. 112
Stack sorting 285
Stack sorting in series 310
Stack sorting, (right) greedy 285
Stack sorting, left greedy 311
Standard deviation 235
Standard Young tableau 214
Stanley — Wilf conjecture 133
Stanley — Wilf conjecture, alternative version 134
Stanley — Wilf conjecture, proof of 159
Stirling numbers of the first kind 90
Stirling numbers of the second kind 11
Stirling numbers signless, of the first kind 85
Subsequence 129
Superpattern 206
Superpattern weak 207
Symmetric group 73
Tangent numbers 319
Total relative displacement 40
Transition lemma 97
Transposition 81
Transposition adjacent 116
Tree  145
Tree binary plane 166
Tree decreasing binary 33 293
Tree minimax 34
Truncated adjacency matrix 57
Type of a permutation 79
Ulam's problem 238
Unimodal sequence 16
Valley 24
Variance 233
Wilson's theorem 118
Winning entry 305
Words over an alphabet 168
Words over an alphabet, k-regular 168
x-factorization 34
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