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Bona M. — Combinatorics of permutations
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.


Язык: en

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$d$-finite series      178
$P$-recursive sequence      33 175
$q$-binomial coefficient      58
$q$-log-concavity      68
$q$-multinomial coefficient      58
$q$-unimodality      69
$r$ - Eulerian numbers      32
$r$-derangement      121
$r$-major index      64
$Risk$ algorithm      245
$x$-factorization      34
Algebraic power series      181
Alternating group      78
Andr$\acute{e}$ 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$\ddot{u}$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$\acute{e}$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$\ddot{o}$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, $j$-half-ascending      27
Permutation, $q$-optimal      192
Permutation, $t$-stack sortable      287
Permutation, 2-ordered      64
Permutation, alternating      32
Permutation, Andr$\acute{e}$      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$\ddot{o}$milch's formula      92 113
Schr$\ddot{o}$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, $\beta$(0, 1)      145
Tree, $\beta$(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, $k$-regular      168
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