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| Grimaldi R.P. — Discrete and combinatorial mathematics. An introduction |
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| Предметный указатель |
Invalid argument 85 93 94 127
Invariant (element under a permutation) 815 817
Inventory 821
Inverse (under addition) 280
Inverse (under multiplication) 280
Inverse function 285 A-10
Inverse laws for a Boolean algebra 762
Inverse laws for Boolean functions 737
Inverse laws for Boolean variables 737
Inverse laws for logic 65
Inverse laws for set theory 160
Inverse of an implication 69 85 105—107
Inverses in a group 777 830
Inverses under + in a ring 702
Inverter 745
Invertible function 284—286 290
Irreducible polynomial 844
Irreflexive relation 357
Isobutane 610
Isolated fundamental conjunction 750
Isolated product term 750
Isolated vertex 363 374 530
Isomers 607 610 650 827 832
Isomorphic Boolean algebras 769 773
Isomorphic finite fields 851
Isomorphic graphs 544
Isomorphic groups 785
Isomorphic rings 723
Isomorphism of Boolean algebras 766 768 769 773
Isomorphism of finite fields 851
Isomorphism of graphs 540 544
Isomorphism of groups 785
Isomorphism of rings 723
Iterative algorithm 299 676
Iverson, Kenneth 651
Jean, Roger V. 522 524
Johnson, D.B. 670 695 696
Johnson, Lyle 651
Johnson, Selmer Martin 523 524
Jordan, Marie Ennemond 650
Juxtaposition 316 318
k(G) 534
k-ary operation 313
k-equivalent states 350 388
k-regular graph 551
k-unit delay machine 339 343
Karnaugh map 748—754 773
Karnaugh map don’t care conditions 758—760
Karnaugh, M. 748 773
Karp, R. M. 679
Kempe, Sir Alfred 589
Kepler, Johannes 522
Kernel of a group homomorphism 833
Kernel of a ring homomorphism 729
Kershenbaum, A. 670 695 696
Key (to a record) 720
Khowarizm 238
Kirchhoff s Law 474
Kirchhoff, Gustav 598 607 650
Kitab al-jabr w’al muquabala 239
Kleene closure (of a language) 322 330
Kleene, Stephen Cole 139 140 322
Klein Four group 789
Klein, Felix 831
Kneiphof 551
Knuth, Donald Ervin 311 312 395 396 522—524 651 652
Koch snowflake curve 486
Kohavi, Zvi 343 345 396
Konig, Denes 599
Konigsberg 396 529 535 551—553 598
Kronecker, Leopold 238 730 831
Kruskal, Joseph Bernard 665 694 696
Kruskal’s algorithm 666—668
Kummer, Ernst 731
Kuratowski, Kasimir 563 599
Kuratowski’s Theorem 563 599
L(G) 605
Labeled complete binary tree 639
Labeled directed graph 333
Labeled multigraph 542
Labeling Procedure 676 677 695
Ladas, Garasimos 522 523
Ladder graph 604 654
Lagrange, Joseph-Louis 526 830
Lagrange’s Theorem 792
Lame, Gabriel 522 730
Landau symbol 310
Landau, Edmund 310
Language 202 319—323 343 349 350
Larney, Violet Haclimeister 241 731 732 831 832 872 873
Larson, Harold J. 458
Last-in-first-out structure 502
Latin square (in standard form) 855
Latin squares 835 853—859 861 863 864 872
Lattice 379 733
Lattice point 279
Law of Double Negation 64 65
Law of the Double Complement for a Boolean algebra 764
Law of the Double Complement for Boolean functions 737
Law of the Double Complement for Boolean variables 737
Law of the Double Complement for set theory 160
Law of the syllogism 82 84 88 141 147
Lawler, Eugene L. 585 600 602 694 696
Laws for Boolean functions 737 763
Laws for Boolean variables 737
Laws of logic 64 65 68 73 88 94 160 737 763
Laws of set theory 160 165 737 763
lcm (least common multiple) 230 235
Le Probleme des rencontres 428
Leading coefficient 835
Leaf 614
Least common multiple 230 231
Least element (in a poset) 377
Least element (well-ordered set) 184
Least upper bound (lub) 378
Left child 617
Left coset 791
Left subtree 622 623
Left-cancellation property (in a group) 779
Legendre, Adrien-Marie 730
Leibniz, Gottfried Wilhelm 137 138 308 309
Lemma 215
Length of a chain 399
Length of a cycle (in a graph) 365
Length of a cycle (in group theory) 815
Length of a path 365
Length of a string 23 316 318
Length of a walk 531
Lenstra, J.K. 585 600 602
Leonardo of Pisa 456 521 522
Lesniak, Linda 599 601
Lesniak-Foster, Linda 599 601
Level 615
Level number 615
Levels of gating 748
Levels of infinity 309
LeVeque, William Judson 241
Lewis, Harry R. 343 345
Lewis, James T. 311
Lexicographic order 617
Liber Abaci 456 521
LIFO structure 502
Limit of a real-valued function 113 114
Limit of a sequence of real numbers 121 A-3
Line at infinity 869
Line graph 605
Linear algebra 478
Linear arrangement 6—9 11
Linear combination (integers) 214 226
Linear combination (polynomials) 845
| Linear factor of a polynomial 842
Linear linked lists 720
Linear recurrence relation 463
Linear resistance network 473
Linear time complexity 296 298 304
Linearly independent solutions 471 477
Linked lists 395
List (in a relational data base) 273
Literal 740
Liu, C.L. 45 46 428 429 458 522—524 554 563 572 599 600 602 651 652 691 694—696 817 827 872 873
Lloyd, E. K. 600 601
Lockett, J. A. 585 600 601
Logarithm A-6—A-8
Logarithmic function A-1 A-8 A-9
Logarithmic time complexity 296
Logic 51—140
Logic chip 171
Logic gate 745
Logic network 745
Logic, basic (logical) connectives 52—54 75 100 101
Logic, Laws of Logic 64 65
Logic, logical equivalence 61 63 64 68
Logic, logical implication 79 80 104
Logic, logically equivalent statements 62 64 104
Logic, negation of quantified statements 109 110 113 114
Logic, Principle of Duality 65
Logic, proof 121 123—134
Logic, quantifiers 98—114 120—134
Logic, Rules of Inference 80—93
Logic, statements (and connectives) 51—54
Logic, Substitution Rules 66 67
Logic, Table of Rules of Inference 88
Logic, truth tables 53 56—58 61—66
Logical connectives see “Basic connectives”
Logical equivalence 61 63 64 68
Logical implication 79 80 104
Logically equivalent open statements 105
Logically equivalent statements 62 64 104
Logically implies 78 105
London Mathematical Society 589
Long division of polynomials 839 840
Loop 363 365 367 368 373 530 543 550 569 571
Loop-free graph 365 530
Lovasz, Laszlo 599
Lovelace, Augusta Ada Byron 239 240
Lovelace, Countess of 239 240
Lower bound 378
Lower limit in product notation 235
Lower limit in sum notation 22
Lozansky, Edward 311 312
lub (least upper bound) 378 379
Lucas numbers 183 208 209 461 522
Lucas, Fransois Edouard Anatole 481 522
Lukasiewicz, Jan 619
L’Hospital’s Rule A-2
m-ary tree 628
Maclaurin series 310 418
Maclaurin series for  418
Maclaurin, Colin 310
MacWilliams, F. Jessie 831 832
Main memory 5
Majority rule 797 798
Manohar, R. 728 732
Mapmaker’s problem 571
Mapping 251 (see also “Function”)
Marriage condition 689
Matches 428
Matching 684
Matching theory 683—691 694 695
Matching theory  689
Matching theory assignment problem 688 695
Matching theory complete matching 684
Matching theory deficiency of a graph 689
Matching theory deficiency of a set of vertices 689
Matching theory Hall’s marriage condition 689
Matching theory matching 684
Matching theory maximal matching 689 695
Matching theory system of distinct representatives 687 695
Mathematical definitions see “Definitions”
Mathematical induction 95 183—188 190—194 196 203—210 240 241 322 323 325 382 515 565 629 630 724 725 841 842
Mathematical induction—alternative form 196—199 208 209 233 303 519 552 566 609
Mathematical logic 139
Mathematical theorems 121
Mathematics of finance 485
Matrix A-13—A-24
Matrix product A-16 A-17
Matrix rings 702 703 730
Matrix sum A-14
Matrix, (i, j)-entry A-13
Matrix, addition of matrices A-14
Matrix, additive identity A-15
Matrix, additive inverse A-15
Matrix, associative law of multiplication A-18
Matrix, column matrix A-13
Matrix, column vector A-13
Matrix, commutative law of addition A-14
Matrix, definition A-13
Matrix, determinant A-19—A-23
Matrix, distributive law of scalar multiplication over matrix addition A-15
Matrix, distributive laws of matrix multiplication over matrix addition A-24
Matrix, equality A-14
Matrix, expansion by minors A-23
Matrix, matrix product A-16 A-17
Matrix, matrix sum A-14
Matrix, minor A-22
Matrix, multiplicative identity A-19
Matrix, multiplicative inverse A-19
Matrix, product A-16 A-17
Matrix, row matrix A-13
Matrix, row vector A-13
Matrix, scalar product A-15
Matrix, square matrix A-13
Matrix, sum A-14
Matrix, system of linear equations A-20
Matrix, zero element A-15
Maurocylus, Francesco 240
MAX 235
Max-flow min-cut theorem 676 677 679 695
Maximal chain 399
Maximal element (of a poset) 376
Maximal flow 673
Maximal independent set of vertices 587 655
Maximal matching 689 695
Maxterm 742
Maxwell-Boltzmann model 43
Maybee, John S. 601
McAllister, David F. 139 140 343 345 396 523 524
McCluskey, E. J., Jr. 773
McCoy, Neal H. 732 872 873
Mealy machine 343
Mealy, George H. 343 345
Median 470
Member (of a set) 143
Membership tables 163 164
Memoire sur les conditions de resolubilite des equations par radicaux 830
Memory location 384 385
Mendelson, Elliott 139 140
Menon, P.R. 773
Merge sort 634—638 668
Merge sort algorithm 637 638
Merging algorithm for two sorted lists 635
Messages 794 795
Method of affirming 80
Method of complete induction 196
Method of contradiction 133 134
Method of contraposition 134
Method of denying 83
Method of exhaustion 123 124
Method of generating functions 493—499 501 502
Method of infinite descent 240
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