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Seymour L. — Schaum's Outline of Theory and Problems of Discrete Math |
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Предметный указатель |
Group, homomorphisms 375
Group, quotient 373
Group, symmetric 372
Growth of functions, rate of 65
Hamiltonian 195
Hamiltonian graph 195
Hamiltonian graph, cycle 195
Hamiltonian, logic 486
Hasse diagram 444
Heap 287—290
Homeomorphic graphs 192
Homomorphism of groups 375
Homomorphism of rings 378
Homomorphism of semigroups 369
Horner’s method 63
Huffman 293
Huffman’s algorithm 291
Huffman’s algorithm, code 293
Ideal 377
Idempotent laws 8 451
Identity, element 366
Identity, function 51
Identity, matrix 108
Identity, relation 29
Image of a function 50 375
Implication, logical 87
Impossible event 152
In (identity matrix) 108
incidence 190
Inclusion map 51
Inclusion — Exclusion Principle 139
Indegree 234
Independent, events 156 170
Independent, repeated trials 151 171
Index of a subgroup 373
Indexed sets 58
Induction, mathematical 12 317 450
Induction, transfinite 450
Inequalities 315 334
Infimum (inf) 447 460
Infinite set 61
Initial state 408 419
Injective function 53
Inner product 103
Inorder traversal 282
Input (in a Turing machine) 421
Integer value 54
Integers 315—323
Integers, modulo m 327 374 376
Integral domain 376
Internal nodes 277 290
Intersection of sets 5 11
Inverse, element 366
Inverse, function 53
Inverse, matrix 109 116
Inverse, order 442
Inverse, relation 29
Invertible, functions 53 68
Invertible, matrices 109
Irreducible element in a lattice 454
Irreducible element in a ring 378
Irredundant decompositions 454
Isolated vertex 191
Isomorphic, Boolean algebras 478
Isomorphic, graphs 192
Isomorphic, groups 375
Isomorphic, lattices 453
Isomorphic, ordered sets 449
Isomorphic, rings 378
Isomorphic, semigroups 309
Join 451
Join, irreducible 454
Karnaugh maps 492—497
Kernel (Ker) 375
Kleene 410
Kleene, closure 410 444
Konigsberg bridges problem 194
Kuratowski’s Theorem 202
Labeled graph 196
Labeled graph, digraph 233
Lagrange theorem 373
Language 406 425
Language, regular 407 413
Language, types of 413
last element 446
Lattice 451—453
lcm(a, b) (least common multiple) 323
Least common multiple 323
Length of a path 193 235
Length of a vector 103
Length of a word 405
Level 60 236
Lexicographical order 238 444
Linear bounded automata 415
Linear, equations 107 115
Linear, order 443
Linear, search 64 66
Linearly ordered 443
Linked list 188
LIST 57
List, linked 188
Literal 481
LNR traversal 282
Logarithmic functions 56
Logic 78—92 486
Logic, circuits 486
Logic, gates 486
Logical, equivalence 83
Logical, implication 87
Logical, operations 79
Loop 191 234
Lower bound 447
LRN traversal 282
Machine, finite state 416
Machine, Turing 419 431
MAP 201
Map, dual 204
Mapping of sets 50 372
Mathematical induction 12
Matrices 104—110
Matrices, determinant of 110
Matrices, inverse of 109
Matrices, multiplication 106
Matrices, square 108
Matrix 104—110
Matrix of a relation 30
Matrix, adjacency 205 239
Matrix, augmented 108
Matrix, Boolean 23
Matrix, path 241
Matrix, reachability 241
Maximal, element 446
Maximal, ideal 402
Maximal, rectangle 495
Maxterm 513
Mean 160 176
Meet 451
Member of a set 1
Merge-Sort 66
Minimal, Boolean expressions 483
Minimal, cover 495
Minimal, element 446
Minimal, path 196
Minimal, spanning tree 199
Minterm 483
Modular arithmetic 55 337
Monic polynomial 378
Monoid 367
Multigraph 191
Multiplication of matrices 106
| Mutually exclusive events 152
N (positive integers) 2 315—318
n(-) (number of elements) 9
n-ary relation 37
NAND gate 489
Negation 80
Negation of a quantifier 90
Neighbor 245
Next-state function 408
NLR traversal 282
nodes 188 233 276
Nodes, external 279
Nodes, internal 281
Nonplanar graph 202
Nonsingular matrix 109
NOR gate 489
Norm 103
Normal subgroup 373
NOT gate 487
NOT gate, tree 276
Number, cardinal 61
One-to-one, correspondence 53
One-to-one, function 52
Onto function 53
Operations 364
operations, set 5 13
OR gate 486
Order 315 442
Order in a Boolean algebra 479
Order of a group 371
Order of an element 374
Order, dual 442
Order, inequalities 315
Ordered, pairs 27
Ordered, partitions 140 145
Ordered, rooted tree 237
Ordered, set 442
Ordering, partial 37 442
Outdegree 234
P(n,r) (permutations) 136
Parallel arcs 235
Parametric form 127
Parent 278 294
Partially ordered set 37 442
Partition of a positive integer 445
Partition of a set 11 23 36 44
Partition, ordered 140
Pascal’s triangle 135
Path in a graph 193 235
Path in a graph, matrix 241
Path in a graph, minimal 196
Path in a graph, shortest 196
Path in a graph, simple 193
permutations 136 372
Permutations with repetition 137
PID (principal ideal domain) 377
Pigeonhole Principle 139
Pivot 114
Planar graphs 200—203
Planar graphs, colorings 203
POINTER 188
Polish notation 238
Polynomial 378—382
Polynomial, function 52
Polynomial, monic 378
Polynomial, roots of 380
Poset (partially ordered set) 37 442
Positive integers N 2 315—318
Postfix form 238
Postorder traversal 282
Power set 10 18
Precedes 442
Prefix form 238
Premises 85
preorder traversal 282
Prime implicant 402 484
Prime number 320
Principal ideal 377
Principle of 9 17 451 478
Priority queue 190 286
probability 152—162
Probability, conditional 155
Product, direct 401
Product, fundamental 481
Product, order 444
Product, rule 133
Product, set 27
Production in a grammar 412
Proper subset 3
Proposition 78—82
Proposition, truth table of 80
Propositional, calculus 78—85
Propositional, function 87
Pruning algorithm 253
Pumping lemma 411
Pushdown automata 415
Q (rational numbers) 2
Quantifiers 87—92
Quantifiers, negation of 90
Quasi-order 443
QUEUE 190
Queue, priority 190 286
Quintuple (Turing machine) 420
Quotient, group 373
Quotient, semigroup 368
Quotient, set 36
R (real number system) 2 316
Random variable 159—162
Range of a function 50
Range of a relation 28
Rate of growth 65
Reachable vertex 235
Reachable vertex, matrix 241
Real, line R 316
Real, number system R 2
Recognition of words 409
Recursively defined functions 59 72
Reduced residue system 328
Reflexive relation 32
Region of a map 201
Regular, expression 407
Regular, grammar 414
Regular, graph 197
Regular, language 407
Relation 27—38
Relation, closure of 34
Relation, congruence 325
Relation, equivalence 35
Relation, graph of 29
Relation, matrix of 30
Relative, complement 6
Relative, frequency 152
Relatively prime 328
Remainder, function 55
Remainder, theorem 380
Repeated trials 157 171
Ring 376—378
Ring of polynomials 378—382
Root of a binary tree 276
Root of a polynomial 380
Root of a tree 236
Rooted trees 236
Rooted trees, ordered 237
Row (of a matrix) 104
Row (of a matrix) canonical form 113
Row (of a matrix) equivalence 113
Row (of a matrix) operations 112 125
Row (of a matrix) reduction 112
Sample space 152
scalar 10 379
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