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Stanley R.P. — Enumerative Combinatorics: Volume 2
Stanley R.P. — Enumerative Combinatorics: Volume 2

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Название: Enumerative Combinatorics: Volume 2

Автор: 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 There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results.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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 584

Добавлена в каталог: 18.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(P, \omega)$-partition      359 401
$(P, \omega)-$      (see $(P</a></span> <span class=subjpages><a href=\omega)$"/>-partition)
$a_{a}$      334
$ex_{q}$      305
$\ast$      476
$\bigwedge$-ring      (see Ring X-)
$\Box$      473
$\circ$      352
$\heartsuit$      219
$\mho$      537
$\odot$      533
$\pi\lambda\eta\theta\nu\sigma\muo\zeta$      404
$\S$      449 103 049 213 310 952 213 310 954 213
$\textit{plethysmos}$      404
(3+1)-free poset      (see poset (3+1)-free)
1-Factor      449
abacus      517
Abel polynomial      (see polynomial Abel)
Abel, N.      127
Abelianization, of a formal series      197
Abel’s identity      (see identity Abel’s)
Abhyankar, S.      251
Abramson, M.      275
Action of $\mathcal{G}$ by conjugation      474
Action of $\mathfrak{G}_{n}$ on $S(V^{*})$      475
Action of $\mathfrak{G}_{n}$ on $\bigwedge^{k}V$      475
Action of $\mathfrak{G}_{n}$ on fc-subsets of [n]      355
Action of $\mathfrak{G}_{n}$ on ordered pairs      356
Action of G on X      350
Action transitive      350
Acyclic ADE      248
Acyclic function      (see Function acyclic)
Acyclic orientation      (see Orientation)
Adjacent transposition      (see Transposition adjacent)
Adjoint linear transformation      (see Linear transformation adjoint)
Adjoint representation of $GL(n, \mathbb{C})$      (see representation of \mathbb{C})$"/> adjoint)
Adler, M      506
Aigner, M.      273
Aissen, M.      544
Aitken, A. C.      398 401 405 532 533
Akin, K.      508
Aldous, D.      214 555
Algebra of symmetric functions      (see Symmetric functions algebra
Algebra, descent      548
Algebra, graded      287
Algebra, Hopf      342 401
Algebra, incidence      482
Algebra, incidence of NC      86
Algebra, Lie      (see Lie algebra)
Algebra, nilCoxeter      497
Algebra, of quasisymmetric functions      (see Quasisymmetric functions)
Algebra, Temperley — Lieb      267
Algebraic differential equation      (see Equation algebraic
Algebraic language      (see Language algebraic)
Algebraic series      (see Series algebraic)
Algebraic topology      503
Algebraic, over K[x]      160
Algorithm, Hillman — Grassi      548
Algorithm, RSK      (see RSK-algorithm)
Allouche, J. — P.      254
Almkvist, G.      105 250
Alperin, J. L.      524
Alter, R.      214
Alternating graph      (see Graph alternating)
Alternating permutation      (see Permutation alternating)
Alternating tree      (see Tree alternating)
Anand, H      68
Ando, T.      545
Andre, D.      212 265
Andrews, G. E      68 263 272 403 405 551
Animal, directed      276
Arcs, noncrossing      222
Arcs, nonintersecting      222
Arm length      457
Arrangement, hyperplane      (see Hyperplane arrangement)
Array, two-line      318
Aspect of a plane partition      (see Plane partition aspect
Associahedron      271
Athanasiadis, C. A.      117 135 142 143 263 265
Atkin, A. O. L.      402 406
Augmented      277
Augmented Schur function      (see Schur function augmented)
Austin, T. L.      126
Automaton      201
Aztec diamond      277
Babson, E.      504 542
Baik, J      555
Balanced tableau      (see Tableau balanced)
Ballot sequence      (see Sequence ballot)
Bar — Hillel, Y.      284
Base b expansion      (see Expansion base
Bases, dual      306
Basic sequence      (see Sequence basic)
Basis, integral orthonormal, of A      322
Basis, orthogonal      307
Basis, orthonormal      354
Baxter permutation      (see Permutation Baxter)
Bead configuration      (see Configuration bead)
Becker, H.W.      261 278
Beckwith, D.      272
Beem, E. A.      406
Beissinger, J. S.      106 107 140
Belcher, P.      217
Bell number      (see Number Bell)
Bender, E. A.      65 68 112 403 406 493
Benyon, W.M.      515
Berele, A.      406
Berenshtein      (see Berenstein)
Berenstein, A. D.      436 438 493 545
Bergeron, F.      69 214 279
Berlekamp, E.      267
Bernhart, F.      257
Bernoulli number      (see Number Bernoulli)
Berstel, J.      214 284
Bertram, E. A.      110
Bertrand, J.      212 214
Bessel function      (see Function Bessel)
Bessenrodt, C.      538 554
BEST theorem      (see Theorem BEST)
beta function      (see Function beta)
Bethe lattice      (see Lattice Bethe)
Betrema, J.      264
Bialgebra      342
Bialtemant      335 397
Biedenharn, L. C.      406
Biggs, N.      69
Billey, S. C.      259—261 263 267 551
Binet, J. P. M.      212 214 215
Binet-Cauchy formula      (see Formula Binet-Cauchy)
Binomial poset      (see Poset binomial)
Binomial type      87
Bjorner, A.      107 137 141 270 284 504 542
Blackwell, D. H.      555
Block      79
Block-tree decomposition      (see Decomposition block-tree)
Block-tree theorem      (see Theorem block-tree)
Bloom, D. M.      266
Blum, J.      110
Blum, P.      281
Board      489
Bochner, S.      254
Bolker, E. D.      110
Bollobas, B.      555
Bona, M.      261 275 276
Bonin, J.      274
Borchardt, C. W.      66—69 506
Border strip      (see Strip border)
Border strip decomposition      (see Decomposition border
Border strip tableau      (see Tableau border
Bouc, s.      504
Boulanger, A. H. L.      250
Bousquet — Melou, M      275 276
box      372
Bracketing of a set      177
Bracketing of a set, arbitrary      178
Bracketing of a set, binary      178
Bracketing of a word      169 177
Bracketing of a word, arbitrary      178 239
Bracketing of a word, binary      177
Bracketing, arbitrary      177
Bracketing, binary      177
Branching, complete      313
Bratley, P.      406
Brenti, F      509 545
Bressoud, D. M.      552
Brink, B      283
Bromwich, T. J. I’a.      67 69 144—146 148
Brown, W. G.      215
Bruckman, P. S.      279
Bruhat order      (see Order Bruhat)
Bryan, J.      113
Brylawski, T      490
Brylinski, R. K.      539
Burge, W. H.      400 406 503 504
Burnside, W.      404 406
Burnside’s Lemma      (see Lemma Burnside’s)
BZ-pattern      (see pattern BZ-)
Cadogan, C. C.      543
Calderbank, A. R.      130 543
Cameron, P. J.      133
Canfield, E. R.      132
Capalbo, M      158
Carlitz, L.      68 105 108 114 122 133 155 253 267 280 403 406 513
Carlsen, I.      277
Carmony, L.      216
Carrell, J. B.      399 406
Catalan disease      (see Disease Catalan)
Catalan mania      (see Mania Catalan)
Catalan number      (see Number Catalan)
Catalan, E. C.      212 215
Catalania      256
Cauchy identity      (see Identity Cauchy)
Cauchy, A. L.      397 404 406
Cauchy-Frobenius lemma      (see Lemma Cauchy-Frobenius)
Cauchy-Schwarz inequality      (see Inequality Cauchy-Schwarz)
Cayley graph      (see Graph Cayley)
Cayley, A.      66—69 212 215 272
Cebotarev, N. G.      505
Cell, Schubert      276
Central Delannoy number      (see Number Delannoy central)
Central factorial number      (see Number central
Chain, saturated, in Young’s lattice      312
Chains, product of      464
Chan, C.      115 267
Chandon, J. L.      269
char      442
Character of a finite abelian group      101
Character of a representation of $GL(n, \mathbb{C})$      (see Representation of \mathbb{C})$"/> character
Character table      (see Table character)
Character, skew      469
Character, virtual      353
Characteristic map      (see Map characteristic)
Characteristic polynomial      (see Polynomial characteristic)
Chaundy, T. W      403 406
Chen, W. Y. C.      137 406 522
Chen, Y.M.      519
Chess problem      230 453
Chessboard complex      (see Complex chessboard)
Chevalley, C.      215 251
Chomsky, N.      214 215
Chords, nonintersecting      222 238
Chow, T      157 511 514
Chowla, S.      66 69
Chromatic polynomial      (see Polynomial chromatic)
Chromatic symmetric function      (see Symmetric function chromatic)
Chrystal, G.      215
Chung, F. R. K.      69 274 277 278
Chung, K. L.      265
Chung-Feller theorem      (see Theorem Chung-Feller)
Cigler, C.      68
Ciucu, M      157 275 277
Clark, M. L.      404
Class function      (see Function class)
Clawfree graph      (see Graph clawfree)
Cloud      80
CO      356 361
Coalgebra      342
Code of a partition      (see Partition code
Code of a permutation      (see Permutation code
Code, Pruefer      25
Coefficient, Littlewood — Richardson      338 398 429 446 510
Coefficient, Littlewood — Richardson algebraic interpretations of      432
Coefficient, Littlewood — Richardson equal to one      451
Coefficient, Littlewood — Richardson nonnegativity of      355
Coefficient, Littlewood — Richardson symmetry of      437
Coefficient, middle trinomial      275
Coefficient, q-binomial, unimodality of      475
Cofman, J.      215
Cohn, H.      117 277 403 406
Cohn, P.M.      211 215 251
Coins, ways to stack      228
Coloring      511
Coloring, proper      462
Coloring, proper o-compatible      512
Column-strict plane partition      (see Plane partition column-strict)
Column-sum vector      (see Vector column-sum)
Comajor index      (see Index comajor)
Combinatorial trigonometry      (see Trigonometry combinatorial)
Comet, S.      517
Commutator      471
COMP      357
Compatible, reverse n      358
Complete branching      (see Branching complete)
Complete homogeneous symmetric function      (see Symmetric function complete
Complete matching      (see Matching complete)
Complete symmetric function      (see Symmetric)
Completion of a monoid algebra      196
Completion of the ring A      291
Completion, MacNeille      485
Complex, chessboard      504
Complex, matching      503
complexity      60
Complexity of $\mathcal{K}_{rs}$      82 101
Complexity of certain planar graphs      103
Component of proper algebraic system      (see System proper component
Component, irreducible      51
Component, of $A\in \mathcal{M}(n, r)$      51
Composition theorem      129
Composition, fractional      98
Composition, weak, of (m, n)      184
Compositional formula      3
Compositional formula for exponential structures      47
Compositional formula, permutation version      6
Compositional inverse      (see Inverse compositional)
Comtet, L.      66 213 215
Configuration counting series      (see Series configuration
Configuration, bead      517
Conjugacy class, even      301
Conjugacy class, self-inverse      111
Conjugate of a word      32
Conjugate of an algebraic series      162 247 255
Conjugate partition      (see Partition conjugate)
Connected graph      (see Graph connected)
Content      373
Context-free language      (see Language context-free)
Continued fraction      236
Convergence, of a sequence of formal series      196
Convex position, probability of      233
Convex sequence      (see Sequence convex)
Convexotope      232
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