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| Grimaldi R.P. — Discrete and combinatorial mathematics. An introduction |
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| Предметный указатель |
Biconditional 53 56 62 121—123
Biconnected component 645—647 651
Biconnected graph 645
Big-Oh notation 294—296 310
Biggs, Norman L. 44 46 600 601
Bijective function 280
Binary digits (bits) 5
Binary label 741
Binary number system 218—220
Binary operation 157 202 214 267 617 619
Binary operation associative 268
Binary operation commutative 268
Binary relation 248
Binary rooted tree 617
Binary search (algorithm) 517—519
Binary symmetric channel 794 (see also “Algebraic coding theory”)
Binary tree 628
Binet form 525
Binet, Jacques Philippe Marie 525
Binomial coefficient 27 45 153
Binomial distribution 173
Binomial theorem 26—28 37 45 124 150 178 405 438 449 457
Binomial Theorem (generalized) 439
Bipartite graph 561 580 683 684 689
Birkhoff-von Neumann Theorem 697
Bit(s) 5 772
Blank (space) 317 318
Blocher, Heidi 732
Block 17
Block code 796 (see also “Algebraic coding theory”)
Block designs 865—869
Block in a design 866
Block of a partition 382
Bonaccio 456
Bondy, J. A. 599 601 695
Boole, George 138 139 176 178 735 772
Boolean addition 257
Boolean algebra 735 762—770 772 773 835 871
Boolean algebra, atom 767 773
Boolean algebra, definition 762
Boolean algebra, dual 764
Boolean algebra, isomorphism 766 768 769 773
Boolean algebra, partial order 765—767
Boolean algebra, principle of duality 764
Boolean algebra, properties of 764 765
Boolean algebra, representation theorem 768 773
Boolean algebra, subalgebra 771
Boolean function 736—743 745—754 759 760 772 773
Boolean function, binary label 741
Boolean function, c.n.f. 742
Boolean function, complement 736
Boolean function, conjunctive normal form 741 742 772
Boolean function, d.n.f. 740
Boolean function, disjunctive normal form 740 772
Boolean function, don’t care conditions 758—760
Boolean function, equality 736
Boolean function, exclusive or 745
Boolean function, fundamental conjunction 740
Boolean function, fundamental disjunction 741
Boolean function, incompletely specified 758
Boolean function, independent of a Boolean variable 744
Boolean function, Karnaugh map 748—754 759 760
Boolean function, literal 740
Boolean function, maxterm 742
Boolean function, minimal-product-of-sums representation 753 754 773
Boolean function, minimal-sum-of-products representation 747 756 758—760 773
Boolean function, minterm 741
Boolean function, product 737
Boolean function, product of maxterms 742
Boolean function, Quine — McCluskey method 753
Boolean function, row number 741
Boolean function, self-dual 774
Boolean function, sum 737
Boolean function, sum of minterms 741
Boolean function, symmetric 774
Boolean ring 732
Boolean variable 736
Booth, Taylor L. 773
Borchardt, Carl Wilhelm 650
Boruvka, Otakar 694
Bose, Raj Chandra 858 872
Bose-Einstein model 43
Boson 43
Bound variable 100 112
Boundary condition(s) 462
Boyer, Carl Benjamin 179
Braille (system) 29
Branch nodes 614
Branches 500 616
Breadth-first search 625—627 651
Breadth-first search algorithm 626
Bridge 570
Brookshear, J. Glenn 343 344
Brualdi, Richard 523
Bubble sort 463—466 470 634 635 638
Buckley, Fred 599 601
Burnside’s Theorem 817 820
Busacker, Robert G. 695
Bussey, W. H. 241 872
BUT 54
Butane 610
Byron, Augusta Ada 239 240
Byron, Lord 239
BYTE 5 219
c (continuum) A-36
C(n,r) 19 44
C, C* 153
c.n.f. 742
Calculational techniques for generating functions 436—443
Campbell, Douglas M. 523
Cancellation law of multiplication 213 707 711
Cancellation laws for a Boolean algebra 764
Cancellation laws for a group 779
Cancellation laws of addition (in a ring) 709
Cantor, Georg 156 176—178 309—311 A-32
Cantor’s diagonal method 310 A-32
Cany 332 746
Capacity 671 672 679
Capacity of a cut 674
Capacity of an edge 672
Cardinality (of a set) 144 A-27 A-28
Carroll, Lewis 139
Cartesian product 246 250
Castle 420
Catalan numbers 502 504 505 507 508 522 523
Catalan, Eugene 502 510
Caterpillar 655
Cauchy, Augustin-Louis 831
Cayley, Arthur 428 589 598 607 650 830 831 A-13
Ceiling function ([x]) 253 254 269 629 651
Cell (memory) 5
Cell of a partition 382
Center of a group 784
Center of a ring 733
Chain 399
Chain of subgroups 872
Change of base 218—223
Char (R) 849
Characteristic equation 471
Characteristic function 313
Characteristic of a ring 849 850
Characteristic roots 471
Characteristic sequence 652
Chartrand, Gary 599 601
Chemical isomers 607 610 650 827 832
Chemistry 600 610 827 828
Chessboard 420—426
Child 615
Chinese remainder theorem 728
Chromatic number 431 588—595
| Chromatic polynomial 431 589—595 600
Chu Shi-kie 178
Chvatal, V. 599
Circuit 532 571
Circular arrangement 11 12
Clairaut, Alexis 309
Clark, Dean S. 311
CLIQUE 604
Clique number of a graph 605
Closed (binary) operation 157 267 269—271 318 701 730 735 762 777 778 836 837
Closed interval 153
Closed path 365
Closed switch 72
Closed walk 531 566 569
Closure in a group 777
Cobweb Theorem 523
Cocycle 586
Code word 795 (see also “Algebraic coding theory”)
Coding schemes 795—797 (see also “Algebraic coding theory”)
Coding theory 3 44 173 333 600 601 607 638 872 873
Coding Theory—prefix codes 638—643
Codomain 252
Cohen, Daniel I.A. 45 46 311 312
Collision (in hashing) 720 732
Collison, Mary Joan 241
Color-critical graph 598 650
Column major implementation 259
Column matrix A-13
Column vector A-13
Comb graph 604 605
Combination 19—21 26 44 45 428 523
Combination with repetition 33—36 44 354 440 496 497
Combinational circuit 315
Combinatorial argument 403 404
Combinatorial designs 731 835 853 865 871 872
Combinatorial designs,  -design 865—867 872 874
Combinatorial designs, affine plane 859—864 866—868 872
Combinatorial designs, balanced incomplete block design 865 866 869
Combinatorial designs, block designs 865—869
Combinatorial designs, finite geometry 835 859 862 865 871 872
Combinatorial designs, Latin squares 835 853—859 861 863 864 872
Combinatorial designs, projective plane 867—869 872 873
Combinatorial identity 149 151 290
Combinatorial proof 10 40 51 143 149 259 264
Combinatorics 143 207 601 794
Common divisor 225
Common multiple 230
Common ratio (in a geometric progression or geometric series) 461
Commutative binary operation 268
Commutative group 777
Commutative k-ary operation 313
Commutative law of + in a ring 701
Commutative law of addition for integers 132
Commutative law of addition for real numbers 111
Commutative law of matrix addition A-14
Commutative law of multiplication for real numbers 111
Commutative laws for a Boolean algebra 762
Commutative laws for Boolean functions 737
Commutative laws for Boolean variables 737
Commutative laws for logic 64
Commutative laws for set theory 160
Commutative ring 703 837
Commutative ring with unity 773
Comparison of coefficients 441
Compiler 308 385
Complement of a Boolean function 736
Complement of a graph 540 541
Complement of a set 159 289 290 540
Complement of a subgraph in a graph 613
Complementary -design 874
Complete binary tree 617 628
Complete binary tree for a set of weights 641
Complete bipartite graph 561
Complete directed graph 581
Complete graph  366 368 491 540 580 581
Complete induction 196
Complete inventory 821
Complete m-ary tree 628
Complete matching 684
Complete n-partite graph 606
Complex conjugates 478
Complex numbers (in BASIC) 725—727
Components (of a graph) 366 368 533
Composite function  281
Composite integer 214 223
Composite primary key 275
Composite relation 358 360
Composition of functions 281—285 287
Composition of relations 357 358
Compositions of integers 37—39 150 151
compound statement 52 53
Computational complexity 293—296 511—520 600
Computer 5
Computer addition of binary numbers 746
Computer algorithms and graph-theoretic properties 600
Computer programming 55 600
Computer recognition of a relation 357—362
Computer science 3 4 44 55 70 104 241 245 248 251—253 260 331 333 363 395 396 472 502 600 601 617 701 A-1 A-8
Concatenation of languages 320 321
Concatenation of strings 318
Conclusion 58 77 124 128 129
Conduction electron pairs 43
Congruence 395
Congruence (of triangles) 61
Congruence modulo n 717 732
Congruence modulo s(x) 846 871
Conjugate of a complex number 478 732 733
Conjunction 52
Conjunctive normal form (c.n.f.) 741 742 772
Connected graph 364 533
Connectives see “Basic connectives”
Constant (term) of a polynomial 835
Constant function 261
Constant polynomial 836
Constant time complexity 296
Continuum A-35
Contradiction 58 64 86 156
Contrapositive 69 105—107 376
Contrapositive method of proof 86 133 134
Control circuits 315
Convergence 437
Converse of a quantified implication 122
Converse of a relation 284
Converse of an implication 69 85 105—107
Convex polygon 505
Convolution (of sequences) 443 454 499
Cooke, K.L. 585 600 601
Corollary 124
Coset 791 807 830
Coset leader 808 (see also “Algebraic coding theory”)
Countable set 309 A-27 A-29 A-37
Counterexample 94 95 101—103 107 132 134
Countess of Lovelace 239 240
Counting 3 4 10
Covalency 866
Covering number (of a graph) 603
Covering of a graph 603
Cross product 246—248 271 321
Cryptography 241
cube 567 568
Cubic equation 829
Cubic time complexity 296
Cut (in a transport network) 673
Cut-set 569 571—573 651
Cut-vertex 577
Cycle in a graph 365 532 571—573 578 651
Cycle index for a group 822
Cycle structure representation 820—822 824 826—828
Cyclic group 787 789 847 849
Czekanowski, Jan 694
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