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| Grimaldi R.P., Rothman D.J. — Discrete and Combinatorial Mathematics: An Applied Introduction |
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| Предметный указатель |
Arithmetic expression 460
Arithmetic of remainders 234
Arithmetica 243
Arithmetica Integra 42
Arithmeticorum Libri Duo 244
Arrangement 6—10 15—18 24 26—28 34 36—39 41 149 155 160 266 310 395 402 406 411 436 437 439 462 463 524 525 559 see
Arrangements (with repetition) 7 26 27
Arrangements with forbidden positions 406—410
Array 91 450 501—503
Ars Conjectandi 41
Articulation point 615—621 624
Articulation point algorithm 619 620
ascending order 450 606
Ascent (in a permutation) 220
Aschbacher, Michael 795
ASIC 149
Assembly language 226
Assignment problem 659 668
Assmus, E.F.Jr. 796
Associated directed graph 350
Associated homogeneous relation 471—473 479 480
Associated minor A-20
Associated undirected graph 350 353 517 645 650
Associative binary operation 268
Associative closed binary operation 311
Associative law of addition for integers 113
Associative law of addition for real numbers 97
Associative law of multiplication for integers 221
Associative law of multiplication for matrices A-16
Associative law of multiplication for polynomials 801
Associative laws for a Boolean algebra 736
Associative laws for a ring 673 746
Associative laws for Boolean functions 713
Associative laws for Boolean variables 713
Associative laws for logic 58
Associative laws for set theory 139
Associative property for composition of relations 345
Associative property for function composition 281 282 345 750
Associative property in a group 745 794
Associativity for Cartesian products 248
AT&T Bell Laboratories 188
Atkins, Derek 795
Atkins, Joel E. 623 624
Atom of a Boolean algebra 738—740 743
Augarten, Stan 243 244
Auluck, F.C. 463 507
Automata theory 333
Automated reasoning 119
Auxiliary variables 461
Average-case complexity 295 296
Axiomatic approach to probability 188
Axioms of probability 159 161
Baase, Sara 305 624 625 641 642 667 668
Babbage, Charles 242 243
Bachmann, Paul Gustav Heinrich 304
Back edge (of a tree) 616—619 621
Backtrack(ing) 331 593 596—598 600 616 653 656
Backward edge 650 651 654
Balanced (rooted) tree 601 602
Balanced complete binary tree 605 606
Balanced incomplete block design 825 826
Ball, M.O. 562 575 576
Ballot problem 45
Bare roundhouse 192
Barnette, David 575
Barnier, William J. 333 334
Barr, Thomas H. 693 708 795 796
Barwise, Jon 119 120
Base 2 8 10 16 225 226 227 608
Base (for a number system) 225
Base (for a recursive definition) 211—213
Base (for exponentiation) A-1
Base step 316
Base-changing formula for logarithms A-7
Basic connectives 47—53 56
Basic connectives and (conjunction) 48 50
Basic connectives, but 50
Basic connectives, exclusive or 48
Basic connectives, if and only if (bicondition) 48
Basic connectives, if...then (implication) 48
Basic connectives, iff 48
Basic connectives, inclusive or (disjunction) 48
Basic connectives, nand 56
Basic connectives, negation (not) 48
Basic connectives, nor 56
Basic connectives, or (disjunction) 48
Basis 447
Basis step 195—197 199 201 202 204—208 212—214 218 317
Bayes, Thomas 188 189
Bayes’ Theorem (Extended Version) 173
Bayes’theorem 170 173 188
Beckenbach, Edwin F. 796
Bell numbers 508
Bell, Eric Temple 508
Bellman, R. 562 575
Bellmore, M. 562 574 575
Bemays, Paul 119
Berge, Claude 573 668
Berger, Thomas R. 707 708 831 832
Bernoulli trial 161 178 179 182 430
Bernoulli, Jakob 41 42
Bernoulli, Johann 302
Bertrand, Joseph Louis Frangois 45
Best-case complexity 295
Biconditional 48 51 52 56 104 105
Biconnected component 615 619—621 624
Biconnected component algorithm 619 620
Biconnected graph 615
Big-Oh notation 290 304
Big-omega notation 293 505
Big-theta notation 294 505
Biggs, Norman L. 41 42 574 575
Bijective function 279 283
Binary compare 727
Binary digits (bits) 5 720
Binary heap 637
Binary label 532 716—718 742
Binary number system 225 226
Binary numbers 323 770
Binary operation 136 193 211 267—269 460 589 591 673 674 686 745
Binary operation, associative 268
Binary operation, commutative 268
Binary relation 250 337 see
Binary representation 229 693 778 779
Binary rooted tree 589 590 594 595
binary search algorithm 501—503
Binary sequence 461 462 610 611
Binary string 128 129 188
Binary symmetric channel 762 763 see
Binary tree 488 595 600
Binet form 457
Binet, Jacques Philippe Marie 457
Binomial coefficient 22 23 42 133 217
Binomial distribution 179
Binomial expansion 30 see
Binomial random variable 179 180 182 183 430
Binomial theorem 21—23 42 106 130 180 188 390 421 422 436 443
Binomial Theorem (generalized) 422 443
Bipartite graph 541 542 558 659 660 662—665
Birkhoff — von Neumann theorem 670
Birkhoff, Garrett 377
Bit(s) 5 225 324 610 720 742
Blank (space) 311
Bletchley Park 333
Blocher, Heidi 708
Block code 764 see
Block designs 825—829 832
Block in a design 825—827
Block of a partition 366
Bonaccio 442
| Bond, James 150
Bondy, J.A. 573 575 668
Bonferroni’s inequality 191
Boole, George 118 119 186 188 377 711 742
Boolean addition 346 711
Boolean algebra 711 714 733—743 799 830
Boolean algebra of sets 740 743
Boolean algebra, atom 738—740 743
Boolean algebra, definition 733
Boolean algebra, dual 735
Boolean algebra, Hasse diagram 736—739
Boolean algebra, isomorphism 737 739 740
Boolean algebra, linear combination of atoms 738
Boolean algebra, partial order 737 738
Boolean algebra, principle of duality 735
Boolean algebra, properties 735 736
Boolean algebra, representation theorem 738 739 743
Boolean complement 711
Boolean expression 720
Boolean function 711—727 729—733 738 742 744 796
Boolean function,  719
Boolean function, absorption laws 713
Boolean function, associative laws 713
Boolean function, binary label 716—718
Boolean function, Boolean function for a prescribed table 714 715
Boolean function, c.n.f. 717 718
Boolean function, commutative laws 713
Boolean function, complement 712
Boolean function, conjunctive normal form 717
Boolean function, d.n.f. 715—718 721—724
Boolean function, definition 712
Boolean function, DeMorgan’s laws 713
Boolean function, disjunctive normal form 715
Boolean function, distributive laws 713
Boolean function, dominance laws 713
Boolean function, don’t care conditions 731—733
Boolean function, equality 712
Boolean function, exclusive or 719 720
Boolean function, fundamental conjunction 715—718 721 732 738
Boolean function, fundamental disjunction 717 718
Boolean function, idempotent laws 713
Boolean function, identity laws 713
Boolean function, incompletely specified 731 732
Boolean function, inverse laws 713
Boolean function, Karnaugh map 722—727
Boolean function, law of the double complement 713
Boolean function, literal 715 716 722—726
Boolean function, maxterm 717 718 727
Boolean function, minimal product of sums representation 727
Boolean function, minimal sum of products representation 721 722 724 725 729—733
Boolean function, minterm 716 717 732 738
Boolean function, product 712
Boolean function, product of maxterms 717 718
Boolean function, Quine — McCluskey method 727 742
Boolean function, row number 716
Boolean function, self-dual 744
Boolean function, sum 712
Boolean function, sum of minterms 717
Boolean function, symmetric 744
Boolean multiplication 711
Boolean ring 709
Boolean sum 737
Boolean variable 712 713 724 729
Booth, Taylor L. 742 743
Borchardt, Carl Wilhelm 622 623
Borfivka, Otakar 667
Bose, Raj Chandra 819 831
Bound 292
Bound variable 88 98
Boundary condition(s) 448
Boundary of a region 546—549
Bounded above 605 608
Boyer, Carl Benjamin 189
Brahmagupta 707
Braille system 24
branch node 588
Branches (of a tree) 154 249 331 488 614
Bravo 226
Breadth-first search 598—600 624 653
Breadth-first search algorithm 598 599
Breadth-first spanning tree 599 656
Bridge 550
Bridges of Koenigsberg 513 518 533—535 573
Brookshear, J. Glenn 333 334
Brualdi, Richard A. 506 507
Bubble sort 450—452 455 605 606 609
Buckley, Fred 573 575
Burnside’s Theorem 783—785 796
Busacker, Robert G. 668
Bussey, W.H. 244 831
BUT 50
Butane 584
bye 602
Byron, Augusta Ada 242 243
Byron, Lord 242
BYTE 5 225
c (continuum) A-30 A-31
C(E) 644
C(n, r) 15 41 436
C++ 4 13 369
C++ compiler 253 369
c.n.f. 717 718
Caesar cipher 690 696
Caesar, Gaius Julius 690
Calculational techniques for generating functions 418—431
Calculus 99 A-3 A-6
Call, Gregory S. 304 305
Cambridge University 705
Campbell, Douglas M. 507
cancel 221
Cancellation law of multiplication 678 681
Cancellation laws for a Boolean algebra 736
Cancellation laws for a group 747
Cancellation laws of addition (in a ring) 680
Cantor, Georg 135 186—188 303 304 A-28
Cantor’s diagonal method 303 A-28
Capacity 644
Capacity for a vertex 657
Capacity of a cut 646 665
Capacity of an edge 631 644 645 650 654 657 661 663
Carbon atom 583 584 792
cardinal number A-31
Cardinality (of a set) 124 186 A-23 A-27
Carroll, Lewis 119
Carry 323 324 720 721
Cartesian product 152—154 248 249 251
Case-by-case verification 105
Castle 404
Catalan numbers 36—39 361 490—493 506 507 586 695 696
Catalan, Eugene Charles 38 490 494
Caterpillar 627 628
Cauchy, Augustin-Louis 795 796
Cayley, Arthur 411 565 581 622 623 794 795 A-11
Ceiling function 254 496 602 623
Cell (memory) 5
Cell (of a partition) 366 367 369 372—375
Center of a group 751
Center of a ring 709
Central limit theorem 188
Chain (poset) 381
Chain (transport network) 650
Chain of subgroups 830
Change in state 319
Change of base 225—230
Char(R) 812
Characteristic equation 456
Characteristic function 307
Characteristic of a ring 812
Characteristic roots 456 468
Characteristic sequence 625
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