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| Grimaldi R.P., Rothman D.J. — Discrete and Combinatorial Mathematics: An Applied Introduction |
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| Предметный указатель |
Ring theory, congruence modulo n 689 690
Ring theory, definition 673 674
Ring theory, field 677 678 681 682
Ring theory, group of units 747
Ring theory, homomorphism 697—700 706
Ring theory, ideal 684 700 706
Ring theory, idempotent element 697
Ring theory, integers modulo n 686—696
Ring theory, integral domain 677 678 681 682
Ring theory, isomorphic rings 698 699 704
Ring theory, isomorphism 698
Ring theory, kernel of a homomorphism 704
Ring theory, matrix rings 674 705
Ring theory, multiplicative identity 675
Ring theory, multiplicative inverse 677
Ring theory, proper divisors of zero 675
Ring theory, ring of matrices 674 705
Ring theory, ring of polynomials 799 801
Ring theory, ring properties 679—684
Ring theory, ring with unity 675
Ring theory, subring 682—684
Ring theory, subtraction 680
Ring theory, unit 677
Ring theory, unity 675
Ring with unity 675 801
Ringel, Gerhard 573 576
Rings of Saturn 42
Rinnooy Kan, A.H.G. 562 575 576
Riordan, John 412 444 445
Rise/fall permutation 495 496
Rivest, Ronald L. 504 507 624 625 638 643 654 668 759
Roberts, Fred S. 42 574 576
Robertson, N. 575 576
Robinson, J.A. 86
Roman, Steven 769 796 797 831 832
Rook 404 407
Rook polynomial 404—406 408 410 412 416 510 659
Root extraction 794
Root of a binary ordered tree 488
Root of a polynomial 802 804—806
Root of a tree 587—590
Root of multiplicity 2 805
Rooted binary tree 488 594
Rooted Fibonacci tree 626
Rooted ordered binary tree 488 489 506 596
Rooted tree 587—596 600 601
Rorres, Chris A-21
Rosen, Kenneth H. 42 244 704 708
Ross, Kenneth A. 119 120
Rota, Gian Carlo 412 444 445
Rotating drum 536
Rotations 10 749 781 782 788 791 792
Rothman, Tony 831 832
Rothschild, Bruce L. 305
Roulette 163 164
Round-robin tournament 559
Rouvray, Dennis H. 574 576
Row major implementation 254
Row matrix A-11
Row number 716
Row vector A-11
Royal flush 152
RSA cryptosystem 759—761 795
Ruin problems 506
Rule for Proof by Cases 78
Rule of Complement 159 172
Rule of Conditional Proof 78
Rule of Conjunction 75 78
Rule of Conjunctive Simplification 78 94 137
Rule of Contradiction 76 78
Rule of Detachment 70 71 78 108
Rule of Disjunctive Amplification 78 137
Rule of Disjunctive Syllogism 75 78
Rule of Existential Generalization 117
Rule of Existential Specification 117
Rule of product 4—7 11 14—19 28 29 34 125 142 197 239 248 255 256 261 274 339 341 342 403 567
Rule of sum 3—5 16 19 34 125 132 148 262 264 274
Rule of the Constructive Dilemma 78
Rule of the Destructive Dilemma 78
Rule of Universal Generalization 110—114 126
Rule of Universal Specification 106—113 126
Rules for negating quantified statements 96
Rules of Inference 70—78 83 84 86 107—109 112 113 117 119
Rules of Inference, Law of the syllogism 72 73 78
Rules of Inference, Modus ponens 70 73 75 78
Rules of Inference, Modus tollens 73 76 78
Rules of Inference, Proof by (the method of) contradiction 76 80 84
Rules of Inference, Reductio ad Absurdum 76
Rules of Inference, Rule for proof by cases 78
Rules of Inference, Rule of conditional proof 78
Rules of Inference, Rule of conjunction 75 78
Rules of Inference, Rule of conjunctive simplification 78
Rules of Inference, Rule of detachment 70 78
Rules of Inference, Rule of disjunctive amplification 78
Rules of Inference, Rule of disjunctive syllogism 75 78
Rules of Inference, Rule of the constructive dilemma 78
Rules of Inference, Rule of the destructive dilemma 78
Rules of Inference, Rule of universal generalization 110—114 126
Rules of Inference, Rule of universal specification 106—113 126
Rules of Inference, Table of rules of inference 78
Run 33 34 192 482
Running time 452
Russell, Lord Bertrand Arthur William 119 135 187
Russell’s paradox 135 186 187
Rydell High School 16
Ryser, Herbert John 42 412 668 669 831 832
R[X] 799
S(m, n) 263
s(m,n) 267
S(x,k) 161
Saaty, Thomas L. 668
Sahni, Sartaj 641 642 668 669
Same cardinality (for sets) A-23
Same likelihood 150 158
Same size (for sets) A-23
Sample space 150—155 157—159 161—164 166—172 175—181 183 262 296 402 409 428
Samuel, Pierre 707 708 831 832
Sanders, D.P. 575 576
Sandler, R. 831
Saturated edge 645 649 650
Saturated hydrocarbons 573 581 584
Saturn 42
Scalar product A-12—A-14
Scattering function 694 708
Schedule 815 825
Scholtz, Robert A. 796
Schroeder numbers 495
Schroeder, Ernst 119 377
Schwenk, Allen J. 628
Scientific American 575
Searching (algorithm) 501
Searching process 295 501
Second level of reachability 338
Second-order homogeneous recurrence relations 456—468
Security 693
Seed 689
Sefer Yetzirah (The Book of Creation) 41
Selection 14—16 19—22 26 see
Selection structure 51
Selection with repetition 26—29 32 415 423 485
Self-complementary graph 529 576
Self-dual 735
Self-dual Boolean function 744
Self-orthogonal Latin square 820
Semicircles 40
Semipath 650—653
Sentences 47 48 310
Separation 645
Separation property 646
SEQUENCE 255
| Sequence of pseudorandom numbers 689 690
Sequence recognizer 326 327 332
Sequential circuit 309 see
Serial binary adder 323 324
Series network 65
Seshu, S. 574 576
Set braces 123 124
Set equality 125 126 252 314
Set of all possible outcomes 150
Set of indices 145
Set theory 87 119 123—129 133—155 211 247 303 304 309 311 313
Set theory of strings 309
Set theory, cardinality 124 186 A-23
Set theory, complement of a set 138
Set theory, countable set 164 303 A-24—A-32
Set theory, denumerable set 303 A-24
Set theory, disjoint sets 137 148
Set theory, element 123
Set theory, element argument 126 137 140 144
Set theory, empty set ( ) 127
Set theory, equality of sets 125 126
Set theory, finite set 124 125 186 A-23 A-24
Set theory, generalized intersection of sets 146
Set theory, generalized union of sets 146
Set theory, infinite set 124 186 189 A-23—A-26 A-28 A-30
Set theory, intersection of sets 136 138
Set theory, intuitive definition of a set 123
Set theory, laws of set theory 139 144
Set theory, member 123
Set theory, membership 126
Set theory, membership table 143 144 146
Set theory, mutually disjoint sets 137 148
Set theory, null set () 127
Set theory, power set 128
Set theory, Principle of Duality 141
Set theory, proper subset 124—126
Set theory, relative complement 138
Set theory, set braces 123 124
Set theory, set of indices 145
Set theory, singleton subset 128
Set theory, size of a set 124 A-23
Set theory, subset 124—128 130—132 138 140 141 149
Set theory, superset 138
Set theory, symmetric difference 136
Set theory, uncountable set 303 A-28
Set theory, union of sets 136 138
Set theory, universe 123—128
Set theory, universe of discourse 123—128
Set theory, Venn diagram 141—144 146 148 155
Set theory, well-ordered set 194
Seven Bridges of Koenigsberg 378 513 518 533—535 573
Seyffarth, Karen 412
Seymour, P.D. 575 576
Shamir, Adi 759
Shannon, Claude Elwood 741—743 761 795 797
Sherbert, Donald R. 506 508
Shi-kie, Chu 188
Shier, Douglas R. 623 625 668 669
Shift 690
Shift cipher 691
Shimura, Goro 706
Shmoys, D.B. 562 575 576
Shortest — Path algorithm 667
Shrikhande, S.S. 819 831
Shushu jiuzhang 707
Siblings 588 593 612
Sichuan 707
Sieve method 411
Sigma notation 17 239
Signals 438 439 761
Signed numbers 681 705
Silvestri, Richard 795 797
Simple group 795
Simultaneous solution of a system of congruences 702
Singleton subset 128
Sink in a finite state machine 331
Sink in a transport network 631
Sink state 331
Size of a set 124 A-23
Sloane, Neil James Alexander 195 191
Smallest element 194
Smith, Henry John Stephen 243
Snowflake curve 475
Software development 203
Soifer, Alexander 304 305
Solow, Daniel 119 120
Solution of polynomial equations 830
Solvable group 830
Sorting 506 581 605 606 608
Sorting technique 450
Source in a network 631
Source of a directed edge 349 514
Source program 253 302
Space (blank) 310
Space complexity function 290
Spanning forest 582
Spanning subgraph 521 582 640
Spanning tree 582 596 597 599 631 638 640
Specification statement 369
Spencer, Joel H. 305
Sphere S(x, k) 161 see
Spine (of a caterpillar) 627 628
Split input (for a gating network) 720
Spokes (in the wheel graph) 519 520
Square matrix A-11
Square of a graph 626
Stabilizer 785
STACK 490—492 507 605
Staircase paths 9 130 132
Stanat, Donald F. 333 334 378 507 508
Standard deviation 180 182 183
Standard form of a Latin square 816 817
Stanley, Richard Peter 444 507 508
Star of David 475
Starting state 320 324 329
State diagram 321 324 327
State table 321 322 324 331 372—375
State transition 320 321
Statement 47—121 127 140 311
Statement, compound statement 48 49
Statement, contradiction 53 58
Statement, contrapositive 62 63 92—94
Statement, converse 62 63 82 99
Statement, definitions 52 87 98 103—105 113
Statement, dual (of a) statement 59 62
Statement, if-then decision structure 51
Statement, if-then-else decision structure 51
Statement, inverse 62 63 82 92—94 99
Statement, logical equivalence 56—61 83 95
Statement, logical implication 69—73 75 89 91 95
Statement, logically equivalent statements 56 58 61—64 74 91 97 98
Statement, logically implies 69 92
Statement, negation 48
Statement, negation of quantified statements 92 96 97
Statement, open statement 86 87 89—92 105 106 109 123 126 194 195
Statement, primitive statement 48
Statement, quantified statement 87
Statement, tautology 53 58 59 69
Statement, theorem 105 106 110 112 119
Statement, truth tables 49
Statistics 3 33 175 188 815
Stein, Clifford 504 507 624 625 638 643 654 668
Steiner triple system 829
Steinhaus, Hugo Dynoizy 506 508
Stern, R.G. 562 575 576
Stifel, Michel 42
Stillwell, John 794 797 831 832
Stinson, Douglas R. 831
Stirling numbers of the first kind 267
Stirling numbers of the second kind 29 260 263—265 303 304 370 508 587
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