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| Merris R. — Combinatorics |
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| Предметный указатель |
 -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  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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