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Bona M. — Combinatorics of permutations
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Название: Combinatorics of permutations
Автор: Bona M.
Аннотация: Permutations have a remarkably rich combinatorial structure. Part of the reason for this is that a permutation of a finite set can be represented in many equivalent ways, including as a word (sequence), a function, a collection of disjoint cycles, a matrix, etc. Each of these representations suggests a host of natural invariants (or "statistics"), operations, transformations, structures, etc., that can be applied to or placed on permutations. The fundamental statistics, operations, and structures on permutations include descent set (with numerous specializations), excedance set, cycle type, records, subsequences, composition (product), partial orders, simplicial complexes, probability distributions, etc. How is the newcomer to this subject able to make sense of and sort out these bewildering possibilities? Until now it was necessary to consult a myriad of sources, from textbooks to journal articles, in order to grasp the whole picture. Now, however, Miklos Bona has provided us with a comprehensive, engaging, and eminently readable introduction to all aspects of the combinatorics of permutations. The chapter on pattern avoidance is especially timely and gives the first systematic treatment of this fascinating and active area of research.
This book can be utilized at a variety of levels, from random samplings of the treasures therein to a comprehensive attempt to master all the material and solve all the exercises. In whatever direction the reader's tastes lead, a thorough enjoyment and appreciation of a beautiful area of combinatorics is certain to ensue.
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Рубрика: Математика /
Серия: Сделано в холле
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 2004
Количество страниц: 387
Добавлена в каталог: 23.10.2011
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Предметный указатель
-finite series 178
-recursive sequence 33 175
-binomial coefficient 58
-log-concavity 68
-multinomial coefficient 58
-unimodality 69
- Eulerian numbers 32
-derangement 121
-major index 64
algorithm 245
-factorization 34
Algebraic power series 181
Alternating group 78
Andr 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
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 240
Determinant 55
Dimension of a poset 273
Euler - Mahonian statistic 67
Euler numbers 319
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
F redi - Hajnal conjecture 159
Ferrer's shape 47
Fibonacci number 342
Fibonacci number, generalized 169
Fine number 171
Frequency sequence 198
Frobenius formula 221
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 table 326
Inversion, of a perm, of a multiset 57
Inversion, of a permutation 43
Inversion, of a tree 65
Involution 105
Involution, fixed-point free 105
Involution, vexillary 165
L vy's theorem 95
Lagrange inversion formula 114
Lattice 273
Lattice, complemented 273
Left-to-right maximum 98
Left-to-right minimum 130
Leg length 259
Lexicographic order 281
Log-concave sequence 18
Logarithmic asymptotics 140
Longest increasing subsequence 236
M bius function 244
Major index 52
Major index, of a perm, of a multiset 62
Major index, of a permutation 52
Major index, of a Standard Young 242
Maps, nonseparable rooted 289
Maps, rooted bicubic 157
Markov's inequality 232
Mean 229
Menger's Theorem 276
Motzkin numbers 279 340
Motzkin paths 206
Narayana numbers 171
Normalization 151
Northeastern lattice path 17 170 271
Outer rim 49
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 matrix 75
Permutation statistic 24
Permutation statistic, Euler - Mahonian 68
Permutation statistic, Eulerian 24
Permutation statistic, Mahonian 53
Permutation, -half-ascending 27
Permutation, -optimal 192
Permutation, -stack sortable 287
Permutation, 2-ordered 64
Permutation, alternating 32
Permutation, Andr 35
Permutation, conjugate 80
Permutation, cycle notation of 74
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, 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, 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, two-line notation of 73
Permutation, two-stack sortable 287
Pop-stack 308
Pop-stack, in parallel 312
Postorder 150 292
Product formula 101
Projection, horizontal 219
Projection, vertical 219
QUEUE 300
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
Robinson - Schensted - Knuth alg 245
Row insertion 251
runs 5
Runs, alternating 24
Runs, ascending 5
Runs, tight ascending 38
Schl milch's formula 92 113
Schr der 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, (right) greedy 285
Stack sorting, in series 310
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, (0, 1) 145
Tree, (1, 0) 311
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, -regular 168
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