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Bergeron F., Labelle G., Leroux P. — Combinatorial Species and Tree-like Structures
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Название: Combinatorial Species and Tree-like StructuresАвторы: Bergeron F., Labelle G., Leroux P.Аннотация: The combinatorial theory of species, introduced by Joyal in 1980, provides a unified understanding of the use of generating functions for both labelled and unlabelled structures and as a tool for the specification and analysis of these structures. Of particular importance is their capacity to transform recursive definitions of tree-like structures into functional or differential equations, and vice versa. The goal of this book is to present the basic elements of the theory and to give a unified account of its developments and applications. It offers a modern introduction to the use of various generating functions, with applications to graphical enumeration, Polya theory and analysis of data structures in computer science, and to other areas such as special functions, functional equations, asymptotic analysis and differential equations. This book will be a valuable reference to graduate students and researchers in combinatorics, analysis, and theoretical computer science.
Язык: Рубрика: Математика /Алгебра /Комбинаторика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1998Количество страниц: 457Добавлена в каталог: 10.03.2005Операции: Положить на полку |
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Предметный указатель
Representative of a virtual species 121 Restricted (species) to a cardinality 30 349 Restriction of a total order 343 Rising factorial 170 Robinson's iterative procedure 299 308 Rodrigues formula 184 Root 2 Rooted c-chromatic trees 294 Rooted directed trees 292 Rooted marked trees 292 Rooted oriented trees 285—286 292 Rooted plane trees 168 178 180 190 284 Rooted signed trees 292 Rooted trees 7 10 41 43 58 60 80 100 114 127 132 141 167 178 181 185—186 209 210 211 226 260 278 303 328 409 412 415 417 Rooted trees, (2,3)-rooted trees 198 211 230 Rooted trees, (2,3)-trees 230 244 Rooted trees, (a,b)-trees 243 Rooted trees, asymmetric 322 329 338 Rooted trees, asymmetric, plane 336 Rooted trees, AVL-trees 245 Rooted trees, B-trees 206 Rooted trees, bicolored 206 Rooted trees, binary (plane) 8—10 162 195 235 238 261 373 Rooted trees, binary (plane), complete 235 358 Rooted trees, binary (plane), increasing 344 345 358 359 373 380 Rooted trees, c-chromatic 294 Rooted trees, cyclic see “Mobiles” Rooted trees, directed 292 Rooted trees, G-rooted trees 195 197 213 229 241 262 275 Rooted trees, G-rooted trees, (2,3)-rooted trees 198 211 230 Rooted trees, G-rooted trees, unlabelled 263 276 Rooted trees, H-enriched 193 210 229 Rooted trees, H-enriched, increasing 374—375 Rooted trees, heavy 224 241 390 Rooted trees, homeomorphically irreducible 283 Rooted trees, increasing 344 345 359 367 Rooted trees, increasing, with even fibers 380 Rooted trees, light 224 Rooted trees, m-ary 211 Rooted trees, marked 292 Rooted trees, mixed 292 Rooted trees, ordered 10 167 185—186 190 195 261 284 379 Rooted trees, ordered, increasing 363 374 383 Rooted trees, ordered, with even fibers 381 Rooted trees, oriented 285—286 292 Rooted trees, plane 168 178 185—186 190 191 284 Rooted trees, plane, asymmetric 336 Rooted trees, plane, bicolored 215 Rooted trees, plane, increasing 363 Rooted trees, planted plane (or planar) 167 Rooted trees, planted plane (or planar), increasing 363 Rooted trees, R-enriched 165 169 170 181 201 207 224—228 239 260 273 275 281 329 383 410 424 429 Rooted trees, R-enriched, increasing 341 361—363 371 389—392 Rooted trees, R-enriched, unlabelled 263 275 425 Rooted trees, signed 392 Rooted trees, ternary 211 Rooted trees, ternary, increasing 368 375 380 Rooted trees, unary-binary 254 Rooted trees, unlabelled 141 290 Rotations of a cube 397 406 Sagittal graph of an endofunction 7 Scoins formula 206 215 Secant functions 352 373 Secant numbers 352 359 381 383 Separation of variables, combinatorial 376 Separation of variables, generalized 387 Sequence of binomial type 169 181 187 188 Set partitions 7 44 49 63 86 104 409 411 413 415 417 Set successor 57 Sets 8 50 322 346 409 411 413 415 416 Sets with even cardinality 29 348 409 411 413 415 416 Sets, hereditary finite 338 Sets, multisets 101 Sets, non-empty 10 Sets, odd cardinality 29 348 409 411 413 415 417 Sets, of cardinality 2 8 Sets, of cardinality n 30 Sets, oriented 144 152 334 409 412 416 Sets, totally ordered 342 Signed trees 292 Signed trees, rooted 292 Simple graphs 4 7 28 46 64 71 74 76 100 116 146 151 158 221 259 273 297 308 351 405 409 411 415 Simple graphs, unlabelled 151 297 405 Simplicial complexes 78 Singletons 8 87 98 322 346 409 Singletons of sort i 103 Species characteristic of the empty set 8 346 409 Species of structures 5 Species of structures, atomic 146 154 329 430 431 Species of structures, flat 322 Species of structures, molecular 140 143—147 154 311 314 317—318 328 333 418—420 431 432 Species of structures, multisort 102 199 Species of structures, weighted 82 Stabilizer 396 Standard form of molecular decompositions 142 Standard form of permutations 22 Stereoisomers 288 Stirling formula 248 258 271 Stirling numbers of first kind 53 69 Stirling numbers of second kind 53 69 116 Stirling, asymptotic expansion 272 Strahler order 235 245 Structure 1 Structured words 78 subsets 7 34 99 409—411 413 415 417 Subsets of cardinality k 34 70 Subsets, non-empty 78 Subspecies 120 134 Substitution of (weighted) L-species 348 353 Substitution of index series 43 84 107 Substitution of species 40 410 413 414 416 418 Substitution of virtual species 127 Substitution of weighted multisort species 104 Substitution of weighted species 84 Subtraction of species 120 Sum of (weighted) L-species 347 Sum of A-weighted sets 82 Sum of species 28 410 412 414 416 418 Sum of virtual species 122 Sum of weighted multisort species 104 Sum of weighted species 84 Sum, ordinal 343 Summable family of series 38 Summable family of species 29 37 Summable family of virtual species 123 Summable family of weighted sets 81 90 Superposition of structures 65 Sur, surjections 112 Surjections 115 Symmetric functions 87 Symmetric functions, complete homogeneous 88 Symmetric functions, elementary 333 Symmetric functions, power sum 88 333 Symmetric group 11 399 Symmetric square 296 Symmetric square root 296 Symmetry 321 Tail vertex 62 Tangent functions 352 373 Tangent numbers 352 359 381 383 Taylor — Maclaurin expansion 119 Taylor's formula, generalized 118 Taylor's formula, with integral remainder 358 Temperley's identity 308 Ternary (plane) rooted trees 211 Ternary (plane) rooted trees, increasing 368 376 380 Topological trees 188 285 291 337 Total cardinality 101 Total orders see “Linear orders” Totally ordered sets 342 Touchard's formula 97 Transitive group action 115 324 Transport of structures 2 5 83 102 343 Tree inversion polynomial 297 382 Trees 7 51 58 127 158 178 182 278 293 300 303 410 412 414 Trees, (2,3)-trees 230 244 Trees, (a,b)-trees 243 Trees, AVL 238 245 Trees, B 243 Trees, bicolored 206 Trees, bicolored, R, S-enriched 206 294 Trees, binary search 341 Trees, block-cut-point 380 Trees, c-chromatic 284 Trees, directed 292 Trees, genealogical 188 Trees, homeomorphically irreducible 188 283 291 337 Trees, identity 321 Trees, leftist 246 Trees, marked 292 Trees, mixed 292 Trees, oriented 285—286 Trees, oriented, unlabelled 290 Trees, plane 178 180 182 190 284 Trees, plane, asymmetric 336 Trees, plane, bicolored 215—217 Trees, plane, unlabelled 290 Trees, PQ-trees 242 Trees, pseudo-leftist 246 Trees, R-enriched 178—182 281 335 410 424—429 Trees, rooted see “Rooted trees” Trees, signed 292 Trees, topological 188 283 291 337 Trees, unlabelled 17 279 290 296 Tri-chromatic graphs 100 116 Tri-colored permutations 107 Tri-colorings 10 Triangular cacti 301 305 307 Triangular cacti, pointed 305 Tricomi identity 96 Type generating series 15 84 106 122 Types (isomorphism) according to a sort 110 112 115 364 Unlabelled bicolored plane trees 217 Unlabelled C-rooted trees 263 276 Unlabelled homeomorphically irreducible trees 284 Unlabelled oriented trees 292 Unlabelled plane rooted trees 186 191 Unlabelled plane trees 290 Unlabelled R-enriched (rooted) trees 263 275 410 424—429 Unlabelled rooted trees 141 290 Unlabelled simple graphs 151 297 405 Unlabelled structures 3 12 14 102 277 Unlabelled trees 10 227 236 241 Unrelated species 102 124 Vertebral column 61 Vertebrates 61 68 Vertebrates, bicolored 215 Vertebrates, degenerate 62 Virtual species 121 Virtual species, negative part 123 Virtual species, positive part 123 Virtual species, reduced form 122 148 151—152 Virtual species, strictly 12 Walkup's formula 186 Weight 81 Weight, preserving functions 81 Weighted exponential formulas 96 Weighted L-species 344 Weighted multisort species 104 Weighted sets 81 Weighted species 82 Words 79 Words, abelian 79 Words, circular 79 92 Words, Lyndon 92 98 Wreath of G-structures 313 Wreath product 145 314 X, singletons 8
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