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Merris R. — Combinatorics
Merris R. — Combinatorics

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Название: Combinatorics

Автор: Merris R.

Аннотация:

This book is intended to be used as the text for a first course in combinatorics. the text has been shaped by two goals, namely, to make complex mathematics accessible to students with a wide range of abilities, interests, and motivations; and to create a pedagogical tool, useful to the broad spectrum of instructors who bring a variety of perspectives and expectations to such a course.


Язык: en

Рубрика: Математика/Алгебра/Комбинаторика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 2003

Количество страниц: 576

Добавлена в каталог: 09.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(\nu, k, \lambda)$-design      see balanced incomplete block design
(n,M,d) code      35
2-tree      371
Abbott, E.A.      372 501
Abundant number      84
Acyclic graph      389
Acyclic orientation      396
Acyclic polynomial      384
Adjacency matrix      387 403
Adjacent edges      338
Adjacent vertices      338
Adjoint      see classical adjoint
Adjugate      398 498
al-Khowarizmi, Mohammed ben Musa      100
al-Tusi      12
Algebra of formal power series      272
Algebraic connectivity      402 405
Alternant hydrocarbon      361
Alternating group      see group alternating
Alternating sign theorem      49ff 259
Andrews, G.E.      501
Antiregular graph      417
Anton, H.      501
Apianus, Petrus      12
Appel, Kenneth      378
Arithmetic sequence      53 254
ASCII      39—40
Association for Women in Mathematics      8
Astragali      65
Balakrishnan, V.K.      501
Balanced incomplete block design      463
Barcode      5ff
Barnard, Fred R.      152
Basis of a linear code      424
Basis of a vector space      496
Bayes, Thomas      27
Bayes’s First Rule      26
Beineke, L.W.      502
Bell numbers      132ff 172 201ff 301ff 310 321
Bell, E.T.      132
benzene      240
Berkeley, (Bishop) George      27
Bernoulli numbers      54ff 76 318
Bernoulli, Jakob      54
Berra, Yogi      279
BIBD      see balanced incomplete block design
Big oh      489
Biggs, N.L.      501
Binary code      34 419 462ff
Binary operation      180
Binary word      34 112—113
Binomial coeffcient      43
Binomial probability distribution      29
Binomial theorem      66
Bipartite graph      361 393
Bipartition      361
Birkhoff, G.      360
Birthday paradox      505
Bit      5 34
Blake, William      87
Block of a design      463
Block of a graph      393
Block of a partition      121
Bogart, K.P.      501
Boole, George      422
Boolean, arithmetic      422 495
Boolean, linear combination      424
Boolean, vector space      423
Bose — Einstein model      139
Bose, R.C.      139 451
boundary conditions      321
Bressoud, D.M.      501
Brooks, R.L.      368
Brualdi, R.A.      501
Bruck — Ryser Theorem      458—459 537
Bruck — Ryser — Chowla theorem      466 475
Bruck, R.H.      458 466
Bryan, William Jennings      394
Budapest      19
Burnside, William      197 501
Burnside’s Lemma      197 230
Busby, R.C.      501
By the numbers      340
BYTE      39
Caesar cypher      126
Cameron, P.J.      202
Cardinality      10 21
Cartesian product      394
Catalan numbers (sequence)      17—18 296 334
Catalan, Eugene      17
Cauchy — Binet Determinant Theorem      400 500
Cauchy, Augustin-Louis      197
Cauchy’s identity      251
Cayley table      180ff 459
Cayley, Sir Arthur      180 377
Characteristic polynomial of a homogeneous linear recurrence      323
Characteristic polynomial of a matrix      335 388 401 407 498
Characteristic roots      498ff
Chebyshef, Pafnuti      387
Chebyshev polynomials      387
Check digit (bit)      see parity check digit
Chi-squared      30
Chowla, S.      466
Chromatic number      360 391 417
Chromatic polynomial      360 384 393 403
Chromatic reduction      358 385
Chu Shih-Chieh      12 45 54
Chuck-a-Luck      22
Chu’s Theorem      45ff 126
Classical adjoint      398 498
CLIQUE      348
Clique number      367 417
Closed formula      254 271 279
Closure property      181
Coalesced vertices      358
Coalescence      368
Codebook      438
Cohen, D.I.A.      501
Colbourn, C.J.      501
Color pattern      see pattern
Coloring      218
Companion matrix      335
Complement of a BIBD      472
Complement of a binary code      40
Complement of a binary word      40
Complement of a graph      343
Complete bipartite graph      361
Complete family of mutually orthogonal Latin squares      452
Complete graph      343
Component of a graph      342
Composition of functions      176
Composition of permutations      178
Composition of positive integers      60 282
Conditional probability      26
Conjugate of a partition      79
Connected graph      342 373 392 402 405
Constant weight code      40 462ff
Constantine, G.M.      501
Convex sequence      265
Cook, S.A.      342
Coordinate representation      499
Corneille, Pierre      117
Coset of a permutation group      190
Coset of a vector space      497
Covered vertex      383
Covering number      391
Covering of a graph      391
Crossing edges      see edge crossings
Cuboctahedron      217
Cut-vertex      393
Cvetkovic, D.M.      501
Cycle graph      383
Cycle in a graph      362
Cycle in a permutation      155
Cycle, directed      395—396
Cycle, index polynomial      242ff 300
Cycle, nontrivial      185
Cycle, permutation      185
Cycle, structure      157 213
Cycle, type      157
Cyclic group      188
de Mere, Chevalier      31
de Morgan, Augustus      377
de Parville, H.      333
Decode      34
Decomposition      see composition
Deficient number      315
Degree of a permutation      184 186
Degree of a permutation group      181
Degree of a vertex      338 341
Degree, sequence      341
Delacroix, Eugene      100
Democritus      337
Dependent parameters      464
Derangement      141
Derangement number      141ff 203 228 243 307 317
Descartes, Rene      182
Determinant      227 497 499
Dewar, James      347
Diameter of a graph      364
dictionary order      105 109 119 480
Difference, array      255
Difference, sequence      255
Dihedral group      207 242
DIMENSION      424 496
Dinitz, J.H.      501
Directed arc      395
Directed cycle      395—396
Directed graph      395
Directed path      395
Dirichlet generating function      310ff
Dirichlet, Peter Gustav Lejeune      310
Disconnected graph      346
discrete derivative      255 265 317
Disjoint cycle factorization (notation)      154ff
Distance between binary words      34
Distance between vertices in a graph      364 394
Distinct partitions      291—292 415
Dobinski, G.      203
Dobinski’s formula for the Bell numbers      203 283
dodecahedron      216
Domain      118
Doob, M.      501
Dot product      see scalar product
DOUBLE PRECISION      493
Doubly transitive      199
Dual of a BIBD      472
Dual of a binary code      426 497
Dual of a projective plane      453
Dual of a pseudograph      379
Duality principle      453
Edgar, Hugh      205
Edge of a graph      338
Edge of a polyhedron      210ff
Edge, chromatic number      356
Edge, connectivity      392
Edge, crossings      340 372
Edge, subgraph      357
Efron, Bradley      32
Eigenvalue      392 401ff 498
Eigenvector      498
Einstein, A.      139
Elementary number      90ff 129
Elementary row operations      495
Elementary symmetric function      88f 112 120 128 166 251 298ff 318 401 477 498
Elementary triangle      91
Empirical probability      114
Equivalence, class      133
Equivalence, relation      133
Equivalent codes      42 442
Equivalent colorings      218
Equivalent cycles      154ff
Equivalent Latin squares      459
Equivalent modulo G      195 223 231
Erdoes, P.      344
Erdoes’s theorem      356
Error, correcting code      34 464ff
Error, pattern      437
Euclid      101
Euclidean algorithm      101
Euler numbers      319
Euler totient function      147ff 318
Euler, Leonhard      17 151 217 449 451
Euler’s formula      217 373
Euler’s magic square      449
Euler’s pentagonal number theorem      293
Euler’s theorem      151
Expected value      30
Exponential generating function      303ff
Extended binomial coefficient      285 295
Falling factorial function      90 128—129 167 265 357 367 369
Fary, I.      379
Feller, W.      502
Fermat, Pierre de      74
Fermat’s Little Theorem      74 140 151
Ferrers diagram      79ff 408ff
Ferrers, Norman Macleod      79
fibonacci      19 320
Fibonacci number (sequence)      19 56 64 66 152 264 281 295 320 331 333 394
Fiedler, Miroslav      402 405
Finite projective plane      454
First theorem of graph theory      341 408
Five-color theorem      376
Fixed point      141
Fluctuating permutation      319
For $\cdots$ next      102
Forbidden subgraph      418
Forest      389
Formal derivative      275
Formal power series      271
Four-color theorem      377
Franklin, Benjamin      447
Franklin’s magic square      449
Freeze-dried expression      269ff
Frobenius, Georg      197
Frost, Robert      66 76
Fuller, R.Buckminster      194 216 379
Fullerene      216 379
Fundamental counting principle      2ff
Fundamental Theorem of Arithmetic      6 154
Fundamental theorem of symmetric polynomials      97 128 299 480
Galilei, Galileo      87 267
Garey, M.      342 502
Gauss, Carl Friedrich      45—46 285
Gauss-Jordan elimination      495
General solution      323
Generalized diagonal      459
Generating function      165 244 268 351 415
Generating matrix      429
Generating set of codewords      424
Generator      188
Genus of a graph      382
Geometric sequence      268
Geometric, dual      378
Golay code      437 447 473
Golden ratio      282 295
Golomb, S.W.      127
Gore, Al      100
Graham, Ron      202 349 501—502
Graph      338
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