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| Grimaldi R.P., Rothman D.J. — Discrete and Combinatorial Mathematics: An Applied Introduction |
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| Предметный указатель |
Diagonal 781
Dick, Auguste 707 708
Dickson, Leonard Eugene 243 244
dictionary order 589
Dierckman, Jeffrey S. 623 624
Difference equations 447 see
Differential equations 447
Digital computer 309 320 581 719
Digital devices 329 332
Digraph 349 352 514 see
Dijkstra, Edsger Wybe 632 667 669
Dijkstra’s Shortest-Path Algorithm 631—638
Dinitz, Jeffrey H. 831
Diophantine equation 235 243
Diophantus (of Alexandria) 235 243
Direct argument 114
Direct product of cyclic groups of prime power order 795
Direct product of groups 751
Direct proof 114 115
Directed arrow 514
Directed cycle 351 358 516
Directed edge 321 349 351 514 646 650
Directed Euler circuit 535 536
Directed Euler trail 539
Directed graph 337 344 347 349 350 351 353 357 377 378 488 514 587 631 632 644
Directed graph, arcs 349 514
Directed graph, associated undirected graph 350 353 517
Directed graph, edges 349 514
Directed graph, loop 349 514
Directed graph, nodes 349 514
Directed graph, strongly connected 351 539
Directed graph, vertices 349 514
Directed Hamilton Path 559
Directed path 353 516 588 632 633 646 649 650 652 653
Directed tree 587
Directed walk 516
Dirichlet drawer principle 303 see
Dirichlet, Peter Gustave Lejeune 303 705
Disconnected graph 352 517
Discrete function 448 452 486
Discrete probability 189
Discrete random variable 428 430
Discrete sample space 164 175
Disjoint collection of sets A-29 A-30
Disjoint cycles 786
Disjoint events 159 169 170 172
Disjoint sets 137 148 see
Disjoint subboards 404 405 408 409
Disjunction 48 56 57
Disjunction (logic gate) 719
Disjunctive normal form (d.n.f.) 715 742
dispersion 180
Distance (in a graph) 518 626 631
Distance function 766 767 see
Distinct real roots (for a recurrence relation) 456—464
Distinguishing string 374
Distributions 29 150 263 264 304 370 403 416 444 493
Distributive Law of matrix multiplication over matrix addition A-21
Distributive Law of multiplication over addition for integers 221
Distributive Law of multiplication over addition for real numbers 57
Distributive Law of scalar multiplication over matrix addition A-13
Distributive Laws for a Boolean algebra 734
Distributive Laws for a ring 799
Distributive Laws for Boolean functions 713
Distributive Laws for Boolean variables 713
Distributive Laws for logic 58
Distributive Laws for set theory 139
Divide-and-conquer algorithms 496—503 507 606
Dividend 223
Divides (for integers) 221
Divides (for polynomials) 802
Divides relation 339 737
Division algorithm for integers 221 223 225 232 236 254 274 276 289 686 754 756
Division algorithm for polynomials 803—805 808—810
Division method (for hashing) 694
Divisor for integers 221 223 342 361
Divisor for polynomials 802
Divisors of zero see "Proper divisors of zero"
Doctrine of Chances 411
dodecahedron 548 556 573
Domain (of a function) 175 253 257 270 281 287
Domain (of a relational data base) 271
Dombowski, Peter 831
Domhoff, Larry L. 333 334 778 796
Dominance (for functions) 290 291
Dominance Laws for a Boolean algebra 735
Dominance Laws for Boolean functions 713
Dominance Laws for Boolean variables 713
Dominates (for functions) 290 291
Dominates (on a set) 498
Dominating set 577 730
Domination Laws for logic 59
Domination Laws for set theory 139
Domination number of a graph 577
Domino 121 195 196 470
Don’t care conditions 731—733
Dorwart, Harold L. 831 832
Double induction 306
Double Negation 58
Doubly linked lists 378
Doubly stochastic matrix 670
Dual code 773 see
Dual graph 549 551
Dual network 551—553
Dual of a statement 59 62 140 141 713 735
Duality in a Boolean algebra 713 735
Duality in logic 59
Duality in set theory 140 141
Dyck, Walther Franz Anton von 794
E(X) 111 182 183
East Prussia 533
echo 226
Economics 506
EDGE 349 514
Edge of minimal weight 640
Edge set 349 514
Edge-disjoint paths 658
Edmonds — Karp algorithm 653—657
Edmonds, J. 653 654 669
Efficiency of a coding scheme 764 see
Efficient procedure 200
Efficient tree 611
Einstein, Albert 707
Electric power network 667
Electric switch 711
Electrical engineering 324
Electrical network 551 573 574 581 622
Electronic realizations of Boolean functions 796
Element 123 124 129 135
Element argument 126 137 140 144
Elementary event 158
Elementary subdivision 542 543
Elements 222 237 238 242
Elements of a set 123
Elsayed, E.A. 562 575 576
else 51
Embedded microcontroller 5
Embedding 540 545
Empty language 313
Empty set ( ) 127 128 159
Empty string (A) 310 323
Encoding 763 see
Encoding function 763 764 767 769 771 see
Encoding scheme 610 611
Encryption 690—693
Encryption function 759
Enderton, Herbert B. 189 A-32
Endpoint 660
energy levels 486
England 565
| ENIGMA 333
Enumeration 3 9 41 186 188 385 391 394 411 415 439 622 623 673
Enumeration of nonisomorphic labeled trees 586 587
Epp, Susanna S. 119 120
Equal likelihood 150 151
Equality of Boolean functions 712
Equality of equivalence classes 368
Equality of functions 279
Equality of matrices A-12
Equality of polynomials 799
Equality of real numbers 55
Equality of sets 125 143 367
Equality of strings 311
Equality relation 342 366 377
Equilateral triangle 475
Equivalence class 367 368 371 377
Equivalence problem 378
Equivalence relation 337 342 343 353 366—378 686 695 735 780 782 783 808 830
Equivalence relation, block 366
Equivalence relation, cell 366 367 369 372—375
Equivalence relation, definition 342
Equivalence relation, equivalence class 367 368 371 377
Equivalence relation, partition 366—375 377 378
Equivalence relation, Stirling numbers of the second kind 370
Equivalent codes 778 see
Equivalent finite state machines 327
Equivalent open statements 92
Equivalent states ( ) 338 371
Eratosthenes 243
Erdoes, Paul 276 573 574
Erlanger Programm 795
Error correction (in a code) 767—769 see
Error detection (in a code) 767—769 see
Error in reasoning 74
Error pattern 762 763 771 779 see
Euclid 42 222 232 237 238 242 243
Euclidean algorithm for integers 231—235 289 454 458 459 505 688 760
Euclidean algorithm for polynomials 808
Euclidean geometry 820
Euler circuit 534 535 556
Euler number 495
Euler trail 534 535 556
Euler, Leonard 303 378 443 494 513 533 544 573 705 794 819 831
Eulerian numbers 193 217 218 304 420
Euler’s conjecture (Latin squares) 819
Euler’s phi function 394 395 689 747
Euler’s Theorem on congruence 759 760
Euler’s Theorem on connected planar graphs 546—548 573
Even integer 104 105 113
Even parity string 332
Even, Shimon 490 507
Event 151 158 159 168 171 262
Event, Bernoulli trial 161 178 179 182 430
Event, elementary event 158
Evert, Christine Marie 54
Eves, Howard 119 120 304 305
Excel 117
Exclusive OR 48 56 416 789
Exclusive or ( ) for Boolean functions 719 720
EXCLUSIVE-OR gate 728
Execution speed 290
Exhaustion (Method of) 106
Exhaustive 457 474
Existence of an identity for a group 745
Existence of an identity for a ring 673
Existence of inverses in a group 745
Existence of inverses under + for a ring 673
Existential generalization 117
Existential quantifier ( ) 87 88 94 96 98
Existential specification 117
Expansion by minors A-20
Expectation 177
Expected value 177 179 180
Experiment 150—154 157 159 162 163 166 167 175 178 180 183
Explicit formula 210 211
Explicit quantifier 89 90
EXPONENT A-1 A-2
Exponential function 402 A-1 A-5
Exponential generating function 436—439 443 444 474
Exponential order 293
Exponential time complexity 293
Exponentiation algorithm 297—299
Extension of a function 257
f 712
f is dominated by g 290 291 341
f is dominated by g on S 498
f(A) 253
f(x) is congruent to g(x) modulo s(x) 808
f-augmenting path 650—654 656 663
Factor of a polynomial 802 804 805
Factor Theorem 804 805
Factorial 6 7 215
Factorial order 293
Factorial time complexity 293
Factorization of a polynomial 805
Failure 161 178
Fallacy 74 75 110
False assumption 115
Fan 628
Fano, Gino 820 831
Feit, Walter 795
Feller, William 444 506 507
Fence 508
Fendel, Daniel 119 120
Fermat’s Last Theorem 705 706
Fermat’s theorem on congruence 759
Ferrers graph 435 443
Ferrers, Norman Macleod 443
Fibonacci generator 697
Fibonacci numbers 193 215—217 219 246 442 447 457 458 463 468 470 477 506 628
Fibonacci relation 442 457 505
Fibonacci sequence 505
Fibonacci trees 626
Fibonacci, Leonardo 506
Field 677 678 681 682 688 707 746 794 802 830 831 see
Field theory 831
Fields (in a record) 694
FIFO structure 598
Filius Bonaccii 442
Finite affine plane 820
Finite Boolean algebra 740 743 799 830
Finite field 799 803 806 811 812 817 820 822 826 830
Finite function 247 284 302 332
Finite geometry 799 820 822 825 830 831 see
Finite group 795
Finite group theory 831
Finite integral domain 682
Finite language 314
Finite poset 377
Finite projective geometry 831
Finite projective plane 831
Finite sample space 164
Finite sequence of n terms A-25
Finite sequence of undirected edges 351
Finite set 124 125 186 280 287 344 A-23 A-24
Finite slope 821
Finite state machine 309 319—324 326—333 337 338 371—376 378 682 720
Finite state machine,  371
Finite state machine,  371 374
Finite state machine, 1-equivalent states 371
Finite state machine, arc 321 329
Finite state machine, definition 320
Finite state machine, directed edge 321
Finite state machine, distinguishing string 374
Finite state machine, E 371
Finite state machine, equivalent machines 327
Finite state machine, equivalent states 338
Finite state machine, first level of reachability 338
Finite state machine, input 320 322 324 329
Finite state machine, input alphabet 320 321
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