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Charalambides C.A. — Enumerative Combinatorics
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Название: Enumerative CombinatoricsАвтор: Charalambides C.A. Аннотация: Enumerative Combinatorics presents elaborate and systematic coverage of the theory of enumeration. The first seven chapters provide the necessary background, including basic counting principles and techniques, elementary enumerative topics, and an extended presentation of generating functions and recurrence relations. The remaining seven chapters focus on more advanced topics, including, Stirling numbers, partitions of integers, partition polynomials, Eulerian numbers and Polya's counting theorem.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2002Количество страниц: 609Добавлена в каталог: 18.11.2009Операции: Положить на полку |
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Partition (s) of a finite set enumeration of 66 273 274 Partition (s) of integers conjugate 386 Partition (s) of integers definition of 370 Partition (s) of integers Ferrers diagram of 386 Partition (s) of integers for the numbers of 377 378 Partition (s) of integers generating function for the numbers of 374 375 511 Partition (s) of integers interrelations among partition numbers 383—385 387 Partition (s) of integers into even number of parts 381 Partition (s) of integers into even number of unequal parts 381 389 Partition (s) of integers into even parts 379 Partition (s) of integers into even unequal parts 398 Partition (s) of integers into odd number of parts 381 Partition (s) of integers into odd parts 379 Partition (s) of integers into odd unequal parts 398 Partition (s) of integers into parts of restricted size 380 396 398 Partition (s) of integers into specified parts 382 Partition (s) of integers into unequal parts 378 Partition (s) of integers into unequal parts of restricted size 400 Partition (s) of integers parts 381 389 Partition (s) of integers, perfect 401 Partition (s) of integers, recurrence relation for the number of 371 373 Partition (s) of integers, self-conjugate 386 Partition (s) of integers, table for the numbers of 372 373 Partition polynomial(s) of an arithmetical function 416 Partition polynomial(s), convolution of 448 Partition polynomial(s), exponential Bell 412 452 466 473 490 505 Partition polynomial(s), expressed by partial Bell 430 Partition polynomial(s), general 419 Partition polynomial(s), logarithmic 424 Partition polynomial(s), partial Bell 412 466 473 Partition polynomial(s), potential 428 431 451 Partition polynomial(s), recurrence relation of 415 Partition polynomial(s), table of 417 Partitions of ordered pairs of integers 403 Pascal’s triangle 55 Perfect partitions 401 Permutation(s) by ascending runs 530 Permutation(s) by cycles 464 465 Permutation(s) by fixed points 170 172 Permutation(s) by inversions 541 Permutation(s) by partially ordered cycles 472 473 475 Permutation(s) by peaks 541 Permutation(s) by ranks 175 Permutation(s) by records 540 Permutation(s) by successions 177 179 Permutation(s) by transpositions 189 Permutation(s) with limited repetition generating function for the number of 214 Permutation(s) with repetition generating function for the number of 213 Permutation(s) with restricted repetition enumeration of 164 Permutation(s), ascending runs of 530 Permutation(s), cycle decomposition of 463 Permutation(s), cyclic with restricted repetition 505 Permutation(s), definition of 40 Permutation(s), enumeration by ordered cycles 474 Permutation(s), enumeration of 47 49 Permutation(s), even 469 Permutation(s), falls of 531 Permutation(s), fixed points of 169 Permutation(s), general generating function for the number of 210 Permutation(s), generating function by number of cycles 466 467 Permutation(s), generating function by number of partially ordered cycles 474 477 Permutation(s), generating function by the number of non-descending runs 537 Permutation(s), generating function for the number of 193 Permutation(s), non-descending runs of 533 Permutation(s), odd 469 Permutation(s), order of 491 Permutation(s), rank of 174 Permutation(s), recurrence relation for the number of 45 46 Permutation(s), restricted enumeration by cycles 465 Permutation(s), rises of 531 Permutation(s), succession of 176 Permutation(s), universal generating function by number of cycles 484 Pigeonhole Principle 38 Polya counting theorem 502 Population 86 Power set 4 Power sum symmetric functions 427 432 458 Principle of addition 16 Principle of inclusion and exclusion 134 136 Principle of multiplication 20 Principle of pigeonhole 38 Principle of reflection 78 Principle of the want of sufficient reason 24 Priority lists 349 probability 26 Probability distribution, binomial 88 218 Probability distribution, binomial moments of 218 Probability distribution, factorial moments of 217 Probability distribution, geometric 217 Probability distribution, hypergeometric 87 Probability distribution, logarithmic distribution convolution of 287 Probability distribution, moments of 124 Probability distribution, negative binomial moments of 126 Probability distribution, negative hypergeometric 87 Probability, classical 24 PRODUCT 30 q-binomial coefficient(s), defined 404 q-binomial coefficient(s), orthogonality relation 406 q-binomial coefficient(s), recurrence relation of 404 405 q-binomial convolution formula 406 Q-binomial formula 406 q-Eulcrian numbers 540 q-factorial 404 q-factorial convolution formula 406 q-identity 392 q-Lah numbers 409 q-Lah numbers, signless 409 q-negative binomial formula 406 q-number 404 Rank numbers 176 185 Rank numbers, table of 176 Rank of a permutation 174 Recurrence relation, definition of 22 Recurrence relation, general solution of 235 Recurrence relation, linear 233 Recurrence relation, linear complete 233 Recurrence relation, linear homogeneous 233 Recurrence relation, linear with constant coefficients general solution of 248 Recurrence relation, particular solution of 248 Recurrence relation, solution by generating function 250 Recurrence relation, solution by iteration 235 Recurrence relation, solution by method of characteristic roots 239 Reflection principle 78 Reflection principle, figure 79 Regions of a plane, enumeration of 237 265 272 Relation 7 Relation, equivalence 7 Relation, inverse or reciprocal 7 Round table conference 183 Runs in combinations 98 161 Runs in permutations 97 Sample 86 Sample points 24 Sample space 24 Schlomilch’s formula 290 Schlomilch’s formula for 290 Schlomilch’s formula for associated 323 324 Schlomilch’s formula for asymptotic expression of 323 Schlomilch’s formula for definition of 278 Schlomilch’s formula for explicit expression of 291 Schlomilch’s formula for expressed in terms of the Stirling numbers of the second kind 290 Schlomilch’s formula for generating function of 282 Schlomilch’s formula generating function of 283 Schlomilch’s formula in non-identical Bernoulli trials 283 Schlomilch’s formula non-central 314 Schlomilch’s formula non-central signless 315 331 332 466 Schlomilch’s formula recurrence relation 321 Schlomilch’s formula recurrence relation of 294 Schlomilch’s formula signless 279 280 322 465 471 477 478 483 Schlomilch’s formula signless associated 478 Schlomilch’s formula table of 294 Selection of a central committee 347 Sequence of elements 8 Set 3 Set, cardinal of 14 Set, complement of 10 Set, countable 9 Set, division of 13 Set, empty or null 3 Set, finite 9 Set, infinite 9 Set, infinitely countable 9 Set, partition of 14 Set, uncountable 9 Set, universal 3 Sets, difference of 10 Sets, disjoint 13 Sets, equivalent 9 14 Sets, exchangeable 142 Sets, intersection of 10 Sets, union of 9 Sieve of Eratosthenes 160 Soccer’s results foresight 37 Spread of rumors 101 Stabilizer 493 Statistical mechanics model Bose — Einstein 89 Statistical mechanics model Fermi — Dirac 90 Statistical mechanics model Maxwell — Boltzman 89 Stirling numbers in a Markov chain 300 Stirling numbers of the first kind 204 291 299 328 329 Stirling numbers of the second kind 96 97 150 151 165 202 291 298 299 328 329 340 342 347 368 474 519 533 544 Stirling numbers, associated 165 324 325 365 Stirling numbers, asymptotic expression of 323 Stirling numbers, definition of 278 Stirling numbers, explicit expression of 289 Stirling numbers, generating function of 282 298 Stirling numbers, non-central 188 314 332 341 347 475 Stirling numbers, orthogonality relations 281 Stirling numbers, recurrence relation 321 Stirling numbers, recurrence relation of 293 297 Stirling numbers, table of 295 Stirling’s formula 109 Stochastic model 24 Subfactorials 178 182 185 Subfactorials, defined 172 Subfactorials, generating function of 199 Subfactorials, table of 172 Subset 4 Subsets of a finite set number of 21 116 Succession numbers 179 230 Succession numbers, generating function of 230 Succession numbers, table of 180 Succession of a circular permutation 181 Succession of a permutation 176 SUM 27 Sum of multinomial coefficients 150 165 400 Summation, changing the order of 29 Sums of sums, generating function of 261 Symbolic calculus 198 Symmetric functions, elementary 192 427 432 458 Symmetric functions, homogeneous product sum 432 458 Symmetric functions, power sum 427 432 458 Tangent coefficients 543 Tennis tournament problem 237 Ternary number system 47 Ternary sequences, enumeration of 47 93 Touchard polynomial(s) 442 452 475 Touchard polynomial(s), expressed by Bell polynomials 445 Touchard polynomial(s), generating function of 444 Touchard polynomial(s), recurrence relation of 446 Transportation of products 73 Transposition 189 462 Triangulation of convex polygons 229 Universal set 3 Up-down permutations 543 Vandermonde’s formula 105 Variance of a sequence 216 Venn diagrams 4 Wallis formula 107 Wronski determinant 234
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