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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 There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results.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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Conway, J. H 215 265 Core, p- (see p-core) Cori, R 261 278 Correspondence, costripp 314 Correspondence, Hillman — Grassi 380 401 Correspondence, Robinson-Schensted (see RSK-algorithm) Coxeter group (see Group Coxeter) Coxeter relations 113 Coxeter, H. S. M 215 265 Crapo, H. 142 Curtis, C. W 406 536 Cusick, T. W 278 Cvetkovic, D. M. 69 157 Cycle index 19 Cycle index of symmetric semigroup 83 Cycle index polynomial (see Polynomial cycle Cycle index, augmented 19 Cycle indicator (see Indicator cycle) Cycle lemma (see lemma cycle) Cycle monomial 19 Cycle type of a permutation (see Permutation cycle Cycle, n- (see n-cycle) Cyclic binomial sum 253 D-finite series (see series D-finite) Davenport-Schinzel sequence (see Sequence Davenport-S Davis, M. W 283 de Bruijn graph (see Graph de De Bruijn sequence (see Sequence de De Bruijn, N. G. 68 69 404 406 de la Harpe, P. 260 267 De Riviere, A. 69 71 De Segner, A. 212 217 Dean, R. A. 263 Decidability 214 Decomposition, block-tree 120 Decomposition, border strip 470 Decomposition, reduced 454 Decomposition, symmetric chain 456 Decoste, H. 531 Decreasing subsequence (see Permutation subsequence decreasing) Degree of 160 Degree of a vertex of a plane forest 30 Degree of a vertex of a planted forest 29 Degree of a vertex of a simple graph 77 Degree of an algebraic series 159 Degree sequence, ordered of a planted forest 29 Degree sequence, ordered of a simple graph 77 Degree, x- 164 Deift, P. 555 Delannoy number (see Number Delannoy) Delest, M. — R 258 Deligne, P. 254 Delta operator (see Operator delta) Denef, J 254 Denes, J. 138 Denominator sequence, of an exponential structure 45 Deodhar, V 276 Depth first order (see Order depth Depth, of a square 515 Deque-sortable permutation (see Permutation deque-sortable) Derangement 469 470 489 Derivation 460 Dershowitz, N. 70 130 262 Desarmenien, J. 521 Descent 236 351 Descent algebra (see Algebra descent) Descent of an SYT 361 364 488 Descent set 351 382 404 454 Descent set of an SYT 361 Determinant, Jacobian 207 Determinant, Vandermonde 334 374 397 Determinant, Wronskian 281 Deutsch, E. 257 264 Dey, I. 111 Diaconis, P. 69 555 Diagonal in characteristic p 218 Diagonal of a noncommutative rational series 211 Diagonal of a rational function 179 213 247 Diagonal of a series 179 219 Diagonal, noncommutative 210 214 Diagram of a plane partition (see Plane partition diagram Diagram, Ferrers, shifted 366 Diagram, growth 328 422 426 438 500 502 Diagram, Murasaki 226 Diagram, Puttenham 262 Diagram, Young 226 309 Diagram, Young paths inside 231 Dickins, A. 266 Dicks, W 250 Differentiably finite series (see series D-finite) Differential poset (see Poset differential) Digraph, balanced 54 Digraph, connected 54 Digraph, Eulerian 54 Dihedral group (see Group dihedral) Dimer 240 244 Direct sum decomposition 45 Discriminant 161 165 211 218 219 Disease, Catalan 256 Dissection of a convex polygon 169 234 239 453 Dissection, enumeration of every 176 Dold, A. 105 Dollhopf, J. 513 Dominance order (see Order dominance) Dominant permutation (see Permutation dominant) Domino 240 244 Donaghey, R. 273 Donnelly, R. G. 263 Doob, M. 69 157 Doran, W. F. 511 515 Doty, S 406 Doubilet, P. 65 491 Double rooted tree (see Tree double Doubly-stochastic matrix (see Matrix doubly-stochastic) Dress, A. W. M 66 70 112 Dual bases (see Bases dual) Dual Cauchy identity (see Identity Cauchy dual) Dual Knuth-equivalent (see Equivalent dual Dual RSK algorithm (see RSK algorithm dual) Duchamp, G. 406 Dulucq, S. 138 258 275 278 500 Dumir, V. C. 68 Dumont, D. 106 109 Duncan, D. G. 519 Dvir, Y 538 Dvoretzky, A. 67 70 Dwork, B 105 282 Dyck language (see Language Dyck) Dyck path (see Path Dyck) Dyck word (see Word Dyck) Dynkin, E. B. 534 Edelman, A. 277 Edelman, P. H 130 262 270 276 497 498 Edrei, A. 545 Eggleton, R. B 267 Ehrenborg, R. 514 Ehresmann, C. 399 407 552 Ehrhart polynomial (see Polynomial Ehrhart) Ehrhart quasi-polynomial (see Quasi-polynomial Ehrhart) Eichler, M. 215 Eidswick, J. A. 139 Eigenvalue of Laplacian matrix 59 Eigenvalue, real 244 Eisenstein, G. 213 215 Eisenstein’s theorem (see Theorem Eisenstein’s) Elementary sequence of characters 470 495 Elementary symmetric function (see Symmetric function elementary) Elkies, N. 277 Equation, algebraic differential 248 Equation, Korteweg-de Vries 506 Equation, Painleve II 556 Equivalence, Knuth (see Equivalent Knuth) Equivalent, dual Knuth 415 Equivalent, jeu de taquin 420 Equivalent, Knuth 400 414 437 Erdelyi, A. 67 70 212 Erdos, P. 111 404 407 Erdos, Peter L. 70 137 Eriksson, H. 283 Eriksson, K. 517 Errera, A. 258 Etherington, I. M. H 67 70 212 278 Euler number (see Number Euler) Euler, L 212 215 275 491 Eulerian 54 103 Eulerian polynomial (see Polynomial Eulerian) Eulerian tour (see Tour Eulerian) Evac 425 Evacuation tableau (see Tableau evacuation) Excedance of a path (see Path excedance Expansion, base b 248 Exponential formula 5 Exponential formula for 2-partitions 151 Exponential formula for exponential structures 48 Exponential formula, permutation version 7 Exponential formula, q-analogue 66 Exponential generating functions, product of 1 Exponential polynomial (see Polynomial exponential) Exponential specialization (see Specialization exponential) Exponential structure (see Structure exponential) Extension, linear (see Linear extension) Faa di Bruno, F 65 70 Fabel, K 275 Factorizations, equivalent 93 Farahat, H. K. 517 Favreau, L. 279 Feit, W 401 407 Feller, W 265 Ferrers diagram (see Diagram Ferrers) Fibonacci number (see Number Fibonacci) Fiedler, M 126 Field, generalized Puiseux 251 Filling, Littlewood — Richardson 432 Finite operator calculus 132 Fishburn, P. C. 263 fix 350 394 Flag f-vector 514 Flag h-vector 464 Flag Schur function (see Schur function flag) Flag variety (see Variety flag) Flag, 351 Flexagon 256 Fliess, M 213 215 Flye Sainte — Marie, C. 69 70 Foata, D 65 70 118 119 127 140 Fomin, S. V. 261 282 400 407 497—499 502 517 545 Ford, G. W 120 Forest of rooted trees 23 Forest, free 24 Forest, labeled 459 Forest, planted 23 24 Forest, recursively labeled 92 Forest, rooted 23 Forest, unlabeled plane 30 Forgotten symmetric function (see Symmetric) Formal series (see Series formal) Formanek, E. 250 Formula for 347 Formula, Binet — Cauchy 68 397 Formula, Faa di Bruno’s 65 Formula, hook-content 403 Formula, hook-length 279 376 382 400 Formula, hook-length q-analogue 376 Formula, Hopf trace 504 Formula, Lagrange inversion (see Lagrange inversion formula) Formula, Mehler’s 119 Formula, Weyl character 403 444 Formula, Weyl denominator 444 503 Formula, Weyl dimension 444 Forsyth, A. R. 402 Fortet, R 152 Foster, R. M. 133 Foulkes, H. 404 407 520 541 Fourier transform (see Transform Fourier) Fractional composition (see Composition fractional) Fractional series (see Series fractional) Frame, J. S. 105 400 407 Franel, J 278 Franfon, J 109 127 140 Franz, R 112 Franzblau, D. S. 401 407 Frederickson, H 158 Free group (see Group free) Free monoid (see Monoid free) Freund, J. E. 263 Frieze pattern (see Pattern frieze) Frobenius characteristic map (see Map characteristic) Frobenius image (see Image Frobenius) Frobenius notation (see Notation Frobenius) Frobenius reciprocity (see Reciprocity Frobenius) Frobenius, F. G. 65 70 400 404 407 527 530 Frumkin, A. 531 Fuchs, A. 127 Fulman, J. 113 Fulton, W 399 407 Function on 7 Function on 85 Function, acyclic 126 Function, Airy 556 Function, Bessel 101 Function, Beta 523 Function, class 349 Function, Euler totient 479 489 Function, group reduction 404 Function, idempotent 84 Function, Moebius 268 289 463 480 Function, Moebius of 7 Function, Moebius of of 49 Function, multiplicative on NC 86 Function, P-recursive 188 213 Function, polynomially recursive (see Function P-recursive) Function, quasisymmetric (see quasisymmetric function) Function, Riemann zeta 113 485 Function, Schur (see Schur function) Function, symmetric (see symmetric function) Function, zeta, of an algebraic variety 105 Fundamental quasisymmetric function (see Quasisymmetric function fundamental) Furlinger, J. 272 Furstenburg, H. 213 215 254 Gale, D. 496 Galois group (see Group Galois) Gandhi, J. M 108 Gansner, E. R. 548 550 Gantmacher, F. R. 545 Gap, Hadamard 282 Gardner, M 215 262 Garsia, A. M 68 119 267 407 438 502 515 518 519 548 Garst, P. F. 504 Gasharov, V.N. 512 514 Gauss, C.F. 518 Gaussian elimination, noncommutative 199 Gelfand pattern (see Pattern Gelfand) Gelfand, I. M 134 215 258 270 398 407 Gelfand-Tsetlin pattern (see Pattern Gelfand-Tsetlin) General linear group (see Group general Generalized permutation (see Permutation generalized) Generating function (see Series) Generating tree (see Tree generating) Genji, The Tale of 262 Genocchi number (see Number Genocchi)
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