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Stanley R.P. — Enumerative Combinatorics: Volume 2
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Название: Enumerative Combinatorics: Volume 2Автор: Stanley R.P. Аннотация: This second volume of a two-volume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, D-finite generating functions, noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course on combinatorics, and includes the important Robinson-Schensted-Knuth algorithm. Also covered are connections between symmetric functions and representation theory. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory, including jeu de taquin and the Littlewood-Richardson rule. As in Volume 1, the exercises play a vital role in developing the material. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1999Количество страниц: 584Добавлена в каталог: 18.11.2009Операции: Положить на полку |
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Pergola, E 274 Perlstadt, M. A. 278 Permanent 100 Permutation representation (see Representation permutation) Permutation, 132-avoiding 261 Permutation, 1342-avoiding 243 Permutation, 2-stack sortable 241 Permutation, 213-avoiding 259 Permutation, 2143-avoiding 455 Permutation, 231-avoiding 261 Permutation, 312-avoiding 224 259 261 Permutation, 321-avoiding 224 259 263 267 Permutation, 4231-and 3412-avoiding 243 Permutation, alternating 73 75 520 Permutation, Baxter 225 246 Permutation, Baxter reduced 246 Permutation, code of 259 Permutation, cycle type of 298 Permutation, deque-sortable 274 Permutation, dominant 261 Permutation, generalized 318 Permutation, graphical representation 27 Permutation, lattice 313 400 432 Permutation, shape of 387 Permutation, smooth 243 Permutation, sortable on two parallel queues 225 Permutation, square root of 76 Permutation, stack-sortable 224 Permutation, subsequence of 386 Permutation, subsequence of decreasing 386 Permutation, subsequence of expected length of longest increasing 488 Permutation, subsequence of increasing 246 386 Permutation, subsequence of increasing and decreasing 404 488 Permutation, typical shape of 555 Permutation, u-avoiding 239 247 Permutation, vexillary 455 Permutations, equivalent 79 Petkovsek, M. 216 Pfaff, J. F. 212 Pfaffian 493 Pieri, M. 398 410 Pieri’s rule (see Rule Pieri’s) Pitman, J. 124 Plactic monoid (see Monoid plactic) Planar rhyme scheme 262 Plane (see Plane partition) Plane binary tree (see Tree binary plane) Plane partition 365 Plane partition, aspect of 372 401 Plane partition, asymptotic enumeration 485 Plane partition, column-strict 227 314 Plane partition, diagram of 371 Plane partition, history of 401 Plane partition, number of columns 365 Plane partition, number of rows 365 Plane partition, part of 365 Plane partition, q-enumeration 551 Plane partition, reverse 403 483 Plane partition, reverse symmetric 483 Plane partition, reverse weak 379 Plane partition, self-complementary 486 Plane partition, shape of 365 Plane partition, skew 487 Plane partition, symmetric 369 403 483 Plane partition, symmetry class of 403 551 Plane partition, totally symmetric 485 Plane partition, totally symmetric and self-complementary 485 Plane partition, trace of 365 403 484 Plane partition, with at most r rows 369 Plane partition, with at most r rows and c columns 365 483 Plane S-tree (see Tree plane Plane, r-dimensional 365 402 Plane, rank of 289 Plane, self-conjugate 458 Plane, stable 462 Plane, total 13 66 87 Plane, total binary 14 66 Plethysm 404 447 475 479 480 543 Plethysm, etymology of 404 Plethysm, inner 533 Plethystic inverse (see Inverse plethystic) Plouffe, S. 279 Pole, telephone 72 Poliak, H. 140 Polya theory (see Theory Polya) Polynomial, Abel 87 Polynomial, characteristic of 49 Polynomial, characteristic of 301 Polynomial, characteristic of 86 Polynomial, characteristic of a hyperplane arrangement 96 Polynomial, characteristic of Linial arrangement 91 Polynomial, characteristic of Shi arrangement 96 Polynomial, characteristic of threshold arrangement 73 Polynomial, chromatic, of 73 Polynomial, cycle index 391 Polynomial, Ehrhart 234 Polynomial, Eulerian 77 489 Polynomial, exponential 87 Polynomial, Hermite 119 Polynomial, irreducible 160 219 Polynomial, Kostka 515 Polynomial, Kostka — Foulkes 515 Polynomial, Laguerre 88 118 Polynomial, noncommutative 196 Polynomial, order 378 Polynomial, q-Catalan 237 Polynomial, unimodal 475 Polynomial, with real zeros 463 481 514 545 Polynomial, zeta of 49 Polynomial, zeta of a binomial poset 88 Polynomially recursive function (see Function P-recursive) Polyomino, enumeration 258 Polyomino, parallelogram 239 257 Polytope of degree sequences 107 Poset of direct sum decompositions 237 Poset of intervals of a chain 227 Poset, (3+1)-free 463 Poset, binomial 88 Poset, differential 499 Poset, intersection of a hyperplane arrangement 96 Poset, intersection of the Linial arrangement 91 Poset, intersection of the Shi arrangement 96 Poset, intersection of the threshold arrangement 73 Poset, inversion 325 Poset, locally rank-symmetric 464 Poset, locally self-dual 464 Poset, series-parallel 88 Poset, shuffle 465 Poset, simplicial 124 Poset, triangular 124 Poset, with no 3-element antichain 242 Position, reachable 244 Position, unavoidable 244 Postnikov, A. 134—136 138 139 143 258 259 262 265 268—270 273 Pouget, J. 269 Poupard, Y. 273 Power series (see Series) Power sum symmetric function (see Symmetric function power Power tree (see Tree power) Pragacz, P. 498 504 508 Preorder 33 Priifer code (see Code Priifer) Priifer sequence (see Sequence Priifer) Priifer, H. 66 71 Prime 95 Principal specialization (see Specialization principal) Principle, of inclusion-exclusion 543 Problem, Schroeder’s first 177 213 Problem, Schroeder’s fourth 66 133 178 213 Problem, Schroeder’s second 177 178 213 273 Problem, Schroeder’s third 66 178 213 Problem, Wedderbum-Etherington commutative bracketing 278 Procesi, C. 514 515 538 Proctor, R. A. 403 411 534 550 551 Prodinger, H. 262 Product, Cauchy 382 Product, Hadamard 166 233 Product, Hadamard in characteristic p 218 Product, Hadamard of D-finite series 193 Product, Hadamard of noncommutative series 207 214 248 Product, Hadamard, multivariate 218 Product, heartamard 219 Product, induction 352 Product, internal 476 478 Product, internal basis-free definition of 477 Product, Kronecker 476 Product, tensor 476 Product, wreath 405 449 Proper algebraic system (see System proper Proper coloring (see Coloring proper) Propp, J. G 264 277 403 406 Prouhet, E. 272 Puiseux series (see Series Puiseux) Puiseux, V. 211 216 Puiseux’s theorem (see Theorem Puiseux’s) Pumping lemma (see Lemma pumping) Putnam Competition 278 Puttenham diagram (see Diagram Puttenham) Puttenham, G. 262 Puusa, A. 266 q-binomial coefficient (see Coefficient q-binomial) Quasi-polynomial, Ehrhart 233 Quasisymmetric function 356 382 455 464 482 483 Quasisymmetric function, fundamental 357 384 431 463 Quasisymmetric function, history of 401 Quasisymmetric function, monomial 357 Quasisymmetric functions, algebra of 357 Quotient field of K[x] 160 Quotient field of K[[x]] 160 R-dimensional partition (see Partition r-dimensional) R-partition 46 R. M 404 408 Rabinowitz, S. 404 411 Radoux, C. 267 Rains, E. 133 148 Ramanujan, S. 272 Randall, D 277 random matrix (see Matrix random) Random walk (see Walk random) Randrianarivony, A. 109 Raney, G.N. 67 71 Rank of a group (see Group rank Rank of a partition (see Partition rank Rational language (see language rational) Reachable position (see Position reachable) Read, R, C. 404 411 Reading word (see Word reading) Reciprocity theorem (see Theorem reciprocity) Reciprocity, between sets and multisets 297 Reciprocity, Frobenius 353 Reciprocity, Stirling number 149 Recognizable series (see Series recognizable) Recording tableau (see Tableau recording) Recursively labeled tree (see Tree recursively Redfield, J. H 404 411 537 Reduced decomposition (see Decomposition reduced) Reduced word (see Word reduced) Reducing the number of variables 302 Reflection principle 212 265 Regev, A. 493 538 Regular language (see Language regular) Regular representation (see Representation regular) Reiner, I. 536 Reiner, V. 270 276 411 497 498 504 Relation, nilCoxeter 497 Relation, similarity 264 Remmel, J. B 68 401 403 404 406 411 438 504 519 539 Representation of 443 Representation of 442 Representation of 441 443 Representation of 440 Representation of 440 Representation of 440 Representation of 440 Representation of 440 Representation of 404 440 Representation of 446 Representation of 441 443 Representation of 445 Representation of 445 Representation, induced 396 Representation, linear 395 Representation, permutation 395 Representation, regular 478 Representation, regular of 356 Representation, tensor product 352 476 Reshetikhin, N. Yu. 515 Residue calculus 182 Retakh, V. S. 407 Reutenauer, C. 214 216 261 283 284 410 411 511 521 543 548 Reverse (see Compatible reverse Reverse lexicographic order (see Order reverse Reverse reading work (see Word reverse Reverse semistandard tableau (see Tableau semistandard reverse) ribbon 345 Rice, J. M 266 Rice, S. 0 152 153 Richards, D. 260 Richardson, A. R. 401 403 409 438 544 Richman, D. 285 Rickard, J. 250 Riddell, R. J. 65 71 Riemann zeta function (see Function Riemann Rim hook 345 Rim hook tableau (see Tableau rim Ring, 533 540 Riordan, J. 67 71 108 133 140 152 153 258 Robbins, D. P. 551 552 Roberts, J. 504 Robinson, C. A. 542 Robinson, G. de B 399 400 407 411 438 517 Robinson, R. W. 130 408 543 Robinson, Robin 122 Robinson-Schensted correspondence (see RSK-algorithm) Roby, T. W 400 411 499 500 Rodrigues, O. 212 216 217 Rogers, D. G 213 217 258 260 264 274 275 Roichman, Y. 531 Roman, S. 132 Root, of a structure 10 Roselle, D. P. 262 267 Rosen, J. 68 71 Rosen, M. 105 Rota, G. — G 65 66 71 132 133 142 Routh, E. J. 545 Row insertion (see Insertion row) Row-sum vector (see Vector row-sum) RSK algorithm 260 316 318 382 458 488 503 504 RSK algorithm for (3+1)-free posets 512 RSK algorithm geometric description 327 400 RSK algorithm history of 399 RSK algorithm, dual 331 400 RSK algorithm, reverse 549 Rubel, L. A. 217 282 Rule, jeu de taquin version 429 Rule, Littlewood — Richardson 339 399 506 552 Rule, Littlewood — Richardson history of 438 Rule, local 328 424 Rule, Mumaghan — Nakayama 347 354 515 516 519 520 522 Rule, Mumaghan — Nakayama history of 401
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