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| Grimaldi R.P. — Discrete and combinatorial mathematics. An introduction |
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| Предметный указатель |
Method of undetermined coefficients 483
Methodus Differentialis 310
Metric 799
Metric space 799
Meyer, Paul L. 179
Miller, George Abraham 830
MIN 235
Minimal covering of a graph 603
Minimal distinguishing string 391—393
Minimal dominating set 603 757
Minimal element (of a poset) 376
Minimal product of sums 753 754 773
Minimal spanning tree 665—670 694 695
Minimal spanning tree algorithms 666 669
Minimal sum of products 747 748 756 758—760 773
Minimization process 349 388—393
Minimization process algorithm 389
Minor A-22
Minterm 741
Mirsky, Leon 695 696
MiUbanke, Annabella 239
Mobius inversion formula 428
MOD 228 469
Mod n 717
Modulo n relation 350
modus ponens 80 84 88 126 127 323
Modus Tollens 83 84 86 88 126 127
Moment generating function 457 458
Monary operation 158 267 762
Monic polynomial 884
Monotone increasing function 516
Moon, John Wesley 650 652
Moore, Edward Forrest 343 345 396
Morash, Ronald P. 140
Moser, L. 508 524
Multigraph 363 534 542 657
Multinomial coefficient 28
Multinomial theorem 28 37 124
Multiple of a polynomial 839
Multiple of an integer 213
Multiple output network 746
Multiple root 842
Multiples of group elements 780
Multiplication of equivalence classes of integers (in  ) 718
Multiplication of equivalence classes of polynomials 846 847
Multiplication of polynomials 836
Multiplicative cancellation in  ) 213
Multiplicative identity for matrices A-19
Multiplicative identity for real numbers 120
Multiplicative identity in a ring 703
Multiplicative inverse (of a nonzero real number) 120 280
Multiplicative inverse for a matrix A-19
Multiplicative inverse in a ring 706
Multiplicity of a root 842
Multiplicity of an edge 534
Murty, U.S.R. 599 601 695
Mutually disjoint sets 158 171
n choose r 19
n factorial 7
n! 7 206 298
n!, Stirling’s approximation formula 310
n-Butane 610
n-cube 602
n-fold product 246
n-graph 534
n-tuple 246 272
Nand (connective) 75
NAND gate 754
Napier, John A-7
Natural logarithm A-8
Nearest neighbor 803
Necessary condition 52
Negation 52
Negation of quantified statements 109 110 113 114
Nemhauser, G.L. 585 600 601
Nested multiplication method 308
Network dual 572 573
Network electrical 572 573 607
Network feedback 774
Network gating 315 745 773
Network linear (resistance) 473
Network logic 745
Network multiple output 746
Network parallel 73
Network PERT 372 394
Network Program Evaluation and Review Technique 372 394
Network series 73
Network switching 72—74
Network transport 671
Neutrons 43 497 498
Newsom, Carroll V. 139 140 311 312
Newton, Sir Isaac 310
Next state 328
Next state function 329
Nievergelt, Jurg 523 524
Nine-times repetition code 805 (see also “Algebraic coding theory”)
Niven, Ivan 240 241 458 732
No degree 836
Node 363 530 “Vertices”)
Noether, Emmy 731
Noise (in a binary symmetric channel) 794
Non-Euclidean geometry 859
Nonempty universe 102
Nonhomogeneous recurrence relation 463 471 482—492
Nonlinear recurrence relations 499—504
Nonplanar graph 560—563
Nontrivial subgroup 780
Nor (connective) 75
NOR gate 754
Normal subgroup 831 872
Null child 622
Null graph 541
Null set  148
Number theory 35 214 215 238—241 309 310 409 428 445 701 730
O(g) (order of g) 294
O(g) on 5 513
Object program 252 308
octahedron 568
Octal system (base 8) 218
Odd integer 131
Ohm’s Law 474
Ohm’s Law for electrical flow 598
On the Theory of Groups, as Depending on the Symbolic Equation  830
One element of a Boolean algebra 762
One factor 692
One-terminal-pair-graph 572
One-to-one correspondence 280 309 442 448 505 684 A-27
One-to-one function 255 282 285 290 684
One-unit delay machine 339
One’s complement 220—223
Onto function 260 262—265 271 272 282 285 290 355 384 403 407 408 428 453 526
Open interval 153
Open statement 99 122 123 143 147 184 185
Open switch 72
Open walk 531
operands 157
Operation 157 158
Operations research 600 657 694
Optics 522
Optimal spanning tree 665 666 669 670
Optimal tree 641 642
Optimization 44 248 333 607
Or (connective) 52
Or (exclusive) 434
OR gate 745
Order for the vertices of a tree 620 621
Order g (or Order of g), O(g) 294
Order in a tree 616 617
Order of a group 778
Order of a group element 787 788
| Order of a linear recurrence relation 471
Ordered binary tree 500
Ordered pair 246 250 251
Ordered rooted tree 616
Ordered set A-30
Ordinary generating function 449 (see also “Generating function”)
Ore, Oystein 583 695 696
Organic compounds 827 828
Origin (of an edge) 363 530
Orthogonal Latin squares 854—858 872
Out degree of a vertex 554
Outgoing degree of a vertex 554
Output (for a finite state machine) 328
Output (from a gate) 745 746
Output (from an algorithm) 227 293
Output alphabet 328
Output function 252 329
Overcounting 23 25 428
Overflow error 222
O’Bryant, Kevin 651 652
p is sufficient for q 52
p(m, n), the number of partitions of m into exactly n positive summands 457 458
p(n), the number of partitions of n 445 456
P(n, r) 8 44
Page, E. S. 523 524
Pair of orthogonal Latin squares 854—858
Pairwise disjoint subboards 422
Pairwise incidence matrix 866 867
Palindrome 16 327
Palmer, Edgar M. 600 602
Papadimitriou, Christos H. 343 345
Parallel classes 862—864
Parallel network 73
Parent 615
Parity-check code 797 (see also “Algebraic coding theory”)
Parity-check equations 802 (see also “Algebraic coding theory”)
Parity-check matrix 804 806 807 811
Parker, Ernest Tilden 858 872
Partial fraction decomposition 441 495 496
Partial order 349 353—356 372—379 394 395
Partial order for a Boolean algebra 765—767
Partial ordering relation 353 372 “Poset”)
Partially ordered set 372 (see also «Poset”)
Particular solution 483 484 489 490
Partition 382—386 388 395 717 791
Partitions of integers 36 37 445—448 456—458 523
Pascal program for Euler’s phi function 410
Pascal program for the binary search 518
Pascal program for the bubble sort 464
Pascal program for the calculation of Fibonacci numbers 299
Pascal program for the calculation of Fibonacci numbers (recursive) 489
Pascal program for the Euclidean algorithm 229
Pascal program for the Euclidean algorithm (recursive) 469
Pascal programming language 14 44 55 60 61 104 253 287 301 314 385 468
Pascal, Blaise 45 179 240
Pascal’s triangle 152 153 155 178
Patashnik, Oren 311 312 522 524
Path (in a graph) 365 532 533
Path (staircase) 10 149 151 152
Pattern inventory 817 824—828
Pawlak, Zdzislaw 651
PDP 11 5
Peacock, George 176
Peano, Giuseppe 240 395
Peano’s postulates 240
Peirce, Charles Sanders 138
Pendant vertex 550 569 609
Perfect integer 238
Perfect matching 692
Perfect, H. 695 696
Permutation 6—9 19 20 44 45 408 409 428 449 467 502—504 523
Permutation group 783 815
Permutation matrix 697
PERT network 372 394
Petersen graph 563 590 600
Petersen, Gerald R. 773
Petersen, Julius Peter Christian 600
photons 43
Pi mesons 43
Pi notation 235
Pigeonhole Principle 275—278 290 309 311 338 831
Planar graph 560 599
Planar-one-terminal-pair-graph 572
Planarity of graphs 366 (see also “Planar graph”)
Planck’s constant 43
Platonic solids 567 568
Pless, Vera 831 832
Points at infinity 869
Polaris submarine 372
Polish notation 619
Polya, George 651 652 777 832
Polya’s Method of Enumeration 600 651 812 824—828 832
Polya’s theory in graphical enumeration 600
Polyhedra 598
Polynomial equation 829
Polynomial in the indeterminate x 835
Polynomial ring 837 871
Polynomial time complexity 296
pop 502
POSET 372—379 382 394 397 399 400
Poset antichain 400
Poset chain 399
Poset embedding 397
Poset gib (greatest lower bound) 378 379
Poset greatest element 377
Poset greatest lower bound (glb) 378
Poset Hasse diagram 373—376 394
Poset lattice 379
Poset least element 377
Poset least upper bound (lub) 378
Poset length of a chain 399
Poset lower bound 378
Poset lub (least upper bound) 378 379
Poset maximal chain 399
Poset maximal element 376
Poset minimal element 376
Poset topological sorting algorithm 375—377 394
Poset total order 374—376 394
Poset upper bound 378
Poset well-ordered poset 382
Positive closure of a language 322
Postorder (traversal) 620 651
Power series 435 436 445 457 496
Power set 148
Powers of  316
Powers of a function 284
Powers of a group element 780
Powers of a language 322
Powers of a real number A-1
Powers of a relation 358 359
Powers of an alphabet 316
Powers of strings 318
Precedence graph 364
Precedes 361
Pred (predecessor) function 314
Prefix 319 350 640
Prefix codes 333 640 641 643 651
Prefix notation 619
Pregel River 551
Preimage (of a set) 287—290
Preimage (of an element) 251
Premise 58 77 80 124 129
Preorder (traversal) 620 624 651
Prepositional calculus 763
Prim, Robert Clay 665 694 696
Primary key 275
Prime integer (or number) 134 183 214 719
Prime polynomial 844
Primitive statement 52
Prim’s algorithm 669 670 695
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