Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета
 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям     Bona M. — Combinatorics of permutations Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter 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: 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 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 Реклама     © Электронная библиотека попечительского совета мехмата МГУ, 2004-2021 | | О проекте