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Seymour L. — Schaum's Outline of Theory and Problems of Discrete Math |
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Предметный указатель |
478
(complete bipartite graph) 198
, (complete graph) 197
(integers modulo m) 327
Abelian group 371
Absolute value 54 316
Absorption law 451
Abstraction, Principle of 2
Accepting (yes) states 408
Ackermann function 61
Acyclic 250
Address 237
Adjacency, matrix 205 239
Adjacency, structure (AS) 206 245
Adjacent, fundamental products 492
Adjacent, regions 204
Adjacent, vertices 190 233
Aleph-naught, 61
Algebra of matrices 109
Algebra of propositions 83
Algebra of sets 7 17
Algebra, boolean 477
Algebra, fundamental theorem of 382
Algebraic expression 277
Algorithms 62—66
Algorithms, complexity of 64
Algorithms, division 318
Algorithms, Euclidean 63 322 380
Alphabet 405
Ancestor 278
AND gate 487
AND — OR circuit 488
Antisymmetric relation 33
Apple — Haken Theorem 204
Arcs 233
Arguments 4 23 85
Array 102
Associates 379
Associative operations 365
atoms 454
Augmented matrix 108
AUT(-)(automorphisms) 372
Automaton 408
Automaton, linear bounded 415
Automaton, pushdown 415
Automorphism 372
Average case 64
Backus — Naur form 415
Base value 59
Basic rectangle 494 496
Basic rectangle, maximal 495
Bernoulli trials 158
BFS (breadth-first-search) 209 247
Biconditional statement 84
Big O notation 65
Bijective function 53
Binary search tree 284
Binary search tree, complexity of algorithms 286
Binary tree 276
Binary tree, complete 277
Binary tree, extended 279
Binary tree, similar 277
Binary, addition 417
Binary, digit 117 477
Binary, operation 364
Binary, relation 28
Binary, search 66
Binomial, coefficients 134
Binomial, distribution 159
Bipartite graphs 198
bits 477
Boolean, algebra 477—486
Boolean, expression 481
Boolean, function 491
Boolean, matrix 117 239
Boolean, minimal 483
Boolean, ring 401
Boolean, subalgebra 478
Bounded, lattices 453
Bounded, sets 447
BREADTH-FIRST-SEARCH 209 247
Bridge (in a graph) 194
Bubble sort 66
C(n,r) (combinations) 138
C, complex numbers 2
Cancelation law 367
Cancelation law for congruences 327
Cantor 61
Cantor, theorem 62 74
Cardinal numbers 61—62 70
Cardinal numbers, inequalities 62
Carroll, Lewis 4
Cartesian product 27
Ceiling function 54
Chain 443
Children 278 294
Chinese remainder theorem 332 357
Choice, axiom of 451
Chromatic number 203
Circuit 193 235
Classes of sets 10 18
Classes of sets, residue 326
Closed path 193 235
Closure of relations 34 42
Closure of relations, transitive 242
Closure, Kleene 444
Code 293
Codomain 50
Colored, graphs 203
Colored, maps 223
column 104
Combinations 137 145
Commutative operation 365
Commutative operation, group 371
Comparable elements 443
Complement in a Boolean algebra 477
Complement in a lattice 454
Complement of a set 6
Complemented lattice 454
Complete, binary tree 278
Complete, graph 197
Complete, sum-of-products form 483
Complex numbers C 2
Complexity of algorithms 64
Complexity of algorithms in a binary search tree 286
Complexity of algorithms in a heap 286
Composition of functions 52
Composition of relations 32
compound statement 78
Computable function 422—424 433
Computer representation of binary trees 280
Computer representation of directed graphs 239
Computer representation of graphs 205
Concatenation 405
Conclusion 85
Conditional probability 155 168
Conditional statement 84
Congruence relation 325 345
Congruence relation, arithmetic 326
Congruence relation, equations 329
Conjunction 79
Connected graph 193
Connected graph, components 193
Connected graph, map 201
Connected graph, strongly 235
Connected graph, unilaterally 235
Connected graph, weakly 235
Consensus 484
Consensus, method 485
Consistent enumeration 446 459
| Context-free grammar 414
Context-sensitive grammar 413
Contradiction 82
Contrapositive statement 95
Converse statement 95
Coprime 323
Coset 372
Countable set 62
Counterexample 91
Counting principle 9 133
Cover, minimal 495
Cross partition 23
Cutpoint 194
CYCLE 193 235
Cycle, Hamiltonian 195
Cycle-free 199
Cyclic group 374
d(u,v) (distance) 194
DAG (directed acyclic graph) 250
Degree of a polynomial 378
Degree of a region 201
Degree of a vertex 191 234
DeMorgan’s Law 8 11 90 479
Dense graph 205
Denumerable set 62
Depth of a binary tree 278
Depth of recursion 60
Depth-first-search 209 247
Derivation tree 414
Descendant 278
Detachment, law of 85
Determinants 110—112
Diagonal of a matrix 108
Diagram, Hasse 444
Diagram, state 409 416
Diagram, Venn 3 14
Diameter of a graph 194
dictionary order 444
Digraph (directed graph) 233—235
Digraph (directed graph) matrix of 239
Dihedral group 400
Direct product of groups 401
Directed graph 233—235
Directed graph of a relation 30
Disjoint sets 5
Disjunction (or) 79
Disjunctive normal form 483
Distance between vertices 194
distribution 159
Distribution, binomial 162
Distributive lattice 454
Divisibility 378
Divisibility of integers 319 341
Divisibility of polynomials 379
Division algorithm 318 338
Domain (integral) 376
Domain of a function 50
Domain of a relation 28
Dot product 103
Dual, map 204
Dual, order 442
Duality in a Boolean algebra 478
Duality in a lattice 451
E(G) (edges in a graph) 190
Echelon matrix 113 125
EDGE 190 233
Edge, file 206 246
Edge, parallel 234
Element of a set 1
Elimination, Gaussian 112 125
Empty, relation 29
Empty, set 0 2
Empty, word 405
Endpoints 190
Equality of functions 50
Equality of matrices 104
Equality of sets 1
Equality relation 29
Equipotent 61
Equiprobable space 154 164
Equivalence, class 36
Equivalence, logical 83
Equivalence, relation 35 44 47
Euclidean algorithm 63 322 380
Euler, formula 201 322
Euler, phi function 328 347
Eulerian graph 195
Eulerian graph, trail 195
Event (probability) 152
Event (probability), elementary 152
Event (probability), independent 156 170
Existential quantifier 88
Expectation 64 160 174
Exponential function 55
Expression 419
Expression, algebraic 277
Expression, regular 407
Extended binary tree 279
Extension, Principle of 1
External node 279 290
Factor Theorem 380
Factorial 59 134
Fibonacci sequence 60
Field 376 393
FILE 246
File, edge 206
File, vertex 206
Finite, graph 191
Finite, probability space 153
Finite, set 9 16
Finite, state automaton (FSA) 408 427
Finite, state machine 416
first element 446
Floor function 54
Forest 198 295
Four color theorem 204
Free semigroup 367 406
Free semigroup, order 444
Function 60—71
Function, computable 422—424 433
Function, next-state 408
Function, polynomial 52
Function, rate of growth 65
Function, recursively defined 59
Fundamental product 7 481
Fundamental product, adjacent 492
Gates, logic 486
Gaussian elimination 112
gcd(a,b) (greatest common divisor) 321
General tree 294—295
Generators of a group 374
Godel number 418
Grammar 411 429
Grammar, types of 413
Graph 188
Graph of a function 51
Graph of a relation 29
Graph, adjacency structure (AS) 206 245
Graph, bipartite 198
Graph, complete 197
Graph, connected 193
Graph, directed 233—235
Graph, labeled 196 233
Graph, matrix of 205
Graph, planar 200—203
Graph, regular 197
Graph, weighted 196
Greatest common divisor 63 321
Group 371 386
Group, cyclic 374
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