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Sachkov V.N. — Combinatorial methods in discrete mathematics
Sachkov V.N. — Combinatorial methods in discrete mathematics

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Название: Combinatorial methods in discrete mathematics

Автор: Sachkov V.N.

Аннотация:

This is a presentation of some complex problems of discrete mathematics in a simple and unified form using an original, general combinatorial scheme. The author’s aim is not always to present the most general results, but rather to focus attention on ones that illustrate the methods described. A distinctive aspect of the book is the large number of asymptotic formulae derived. Professor Sachkov begins with a discussion of block designs and Latin squares before proceeding to treat transversals, devoting much attention to enumerative problems. The main role in these problems is played by generating functions, which are considered in Chapter 3. The general combinatorial scheme is then introduced and in the last chapter Polya’s enumerative theory is discussed. This is an important book, describing many ideas not previously available in English; the author has taken the chance to update the text and references where appropriate.


Язык: en

Рубрика: Computer science/Дискретная математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 306

Добавлена в каталог: 22.11.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(v, k, \lambda)$-configuration      25
$\Lambda$-substitution      191
Abelian semigroup      7
Action from the left      213
Action from the right      214
Adjacency matrix      166
Adjacent edges      166
Alternating group      274
Antichain      47
Appell set      113
Arrangement      15
Arrangement with unlimited repetitions      16
ascent      127
Automaton graph      71
Bernoulli polynomial      113
Binary relation      3
Binary relation, composition of      216
Binomial coefficient      17
Block      25
Boolean operation      1
Cartesian product      2
Characteristic polynomial      14
Characteristic root      14
Combination      15
Combination with unlimited repetitions      17
Composition law      6
Composition law, outer      10
Configuration      15
contour      12 167
Contour, elementary      12
Convex hull      61
Convex linear combination      61
Convex poly tope      61
Correspondence, binary      3
Correspondence, functional      3
Covering      264
Covering, k-block      264
Covering, minimal      266
Critical subfamily      50
CYCLE      13 166 187
Cycle class      188
Cycle class, enumerator of      190
Cycle class, maximal      188
Cycle class, minimal      188
Cycle index      272
Cycle of length l      187
Cycle, decrement of      195
Cycle, independent      187
Cycle, length of      13
Cycle, simple      166
Cyclic group      7
Cyclic sequence      144
de Morgan number      115
Decomposition      8
Descent      128
Determinate automaton without input      71
Diagonal      3
Diagram      4
Digraph      4 11 166
Digraph, arc of      166
Digraph, strongly connected      167
Digraph, strongly connected component of      167
Direction of the steepest descent      159
Doubly stochastic matrix      58
Doubly stochastic matrix, multiple      58
EDGE      4 165
Edge, directed      11
Edge, multiple      167
Eigenvalue      14
Eigenvector      14
Elementary matrix      70
Enumerator      229
Enumerator in commutative asymmetric basis      229
Enumerator in non-commutative asymmetric n-basis      240
Enumerator in non-commutative symmetric n-basis      258
Enumerator of exponential type      241
Equivalence class      4
Equivalence relation      4
Euler identity      144
Eulerian number      128
Factor group      9
Factor set      4
Factorial, falling      110
Factorial, rising      110
Fibonacci numbers      77
Finite projective plane      36
Fixed point      11
Forest      166
Formal power series ring      105
Function      5
G-stabilizer      213
Galois number      134
Gaussian coefficient      133
General combinatorial scheme      211 223
General combinatorial scheme, particular case of      223
Generating function      103 107
Generating function, exponential      104
Generating series      107
Generator system      182
GH-equivalence      215
Graph      165
Graph, bicolorable      171
Graph, bipartite      171
Graph, colorable      171
Graph, connected      166
Graph, connected component of      12 166
Graph, labeled      167
Graph, partially labeled      167
Graph, Polya      181
Graph, regular      166
Graph, unlabeled      167
Group      7
Group with finite number of generators      182
Group, orbit of      274
Group, order of      7
Groupoid      7
H-stabilizer      215
Hadamard configuration      36
Hadamard matrix      32
Hadamard matrix, normalized form of      33
Height      12 197
Homomorphism      8
Hyperplane      61
Image      3
Incidence algebra      108 217
Incidence algebra, reduced      109
Incidence algebra, standard      109
Incidence coefficient      109
Incidence matrix      3 6 25
Incident edge      166
Incident vertices      166
INDEX      8
Injective function      290
Input alphabet      293
Integral domain      106
interval      60
Inverse element      7
inversion      126
Isomorphism      8
Latin rectangle      20
Latin rectangle, matrix of      20
Latin square      20
Latin square, based on a group      23
Latin square, matrix of      20
Latin square, normalized      21
Latin square, orthogonal      21
Latin square, seminormalized      22
Loop      167
m-combination      17
m-permutation      16
M-permutation with unlimited repetitions      16
m-sample      223 282
m-sample in commutative asymmetric n-basis      223
m-sample in commutative symmetric n-basis      223
m-sample in non-commutative asymmetric n-basis      223
m-sample in non-commutative symmetric n-basis      223
Mapping, bijective      6
Mapping, discordant      19
Mapping, injective      6
Mapping, many-valued      5
Mapping, single-valued      5
Mapping, surjective      6
Matrix, completely irreducible      98
Matrix, decomposition of      58
Matrix, diagonal of      60
Matrix, Kronecker product of      34
Matrix, minimizing      98
Matrix, non-collinear elements of      60
Matrix, partially reducible      98
Menage problem      75
Moebius function      143 218
Monogenic group      7
Monoid      7
Multigraph      167
Multiplication of substitutions      12
Multiset      212
n-basis      223
Necklace      282
Neutral element      7
Noerlund relation      110
Normal matrix      27
Operation      6
Operation, associative      7
Operation, commutative      7
Operation, distributive      7
Orbit      187 274
Orbit, weight of      289
Order      5
Order, linear      5
Order, partial      4
Ordering, lexicographical      5
Output alphabet      293
Output function      294
p-simplex      63
P. Hall conditions      50
Partially ordered set      5
Partition      139
Partition of number      228
Partition, block of      2
Partition, conjugate      250
Path      11 166
Path, elementary      12
Path, length of      166
Path, simple      166
Permanent rank      80
Permanent, decomposition of, by Laplace formula      74
Permanent, decomposition of, with respect to element      74
Permanent, decomposition of, with respect to row      74
Permutation      15
Permutation matrix      6 13
Polynomial coefficients      18
POSET      5 217
Poset, locally finite      217
Poset, lower bound of      217
Poset, upper bound of      217
Power group      217
Power set      2
Preimage      3
Probabilistic automaton      68
Probabilistic automaton without output      69
Probabilistic transformer      72
Projection      3
Quasigroup      7
Rank, boundary      80
Rank, line      80
Residue class, left      8
Residue class, right      8
Restriction      6
Rhymed sequence      226
Ring      9
Scalar product      14 61
Segment      108
Semigroup      7
Semipermutation matrix      68
Set of states      293
Set, locally finite      108
Set, perfect difference      32
Space, basis of      10
Specification      211
Specification, primary      211 212
Specification, secondary      211 212
Stabilizer      275
Step of formalization      222
Stirling number of the first kind      116
Stirling number of the second kind      116
Stochastic matrix      70
Subgraph      166 167
Subgroup      8
Subgroup, invariant      8
Substitution      6
Substitution, cycle of      187
Substitution, cycle of length l of      187
Substitution, decrement of      195
Substitution, even      195
Substitution, k-regenerative      125
Substitution, non-regenerative      125
Substitution, odd      195
Substitution, orbit of      187
Substitution, transitivity set of      187
Symmetric element      7
Symmetric group      13
System of distinct representatives      49
System of representatives      222
System of representatives, common      56
Transformation      11
Transformation, degree of      11
Transition function      294
Transitivity domain      274
Transpositions of degree n      181
Transpositions, regular product of      183
Transpositions, regular set of      183
Transpositions, support of set of      183
Transversal      49
Transversal, common      56
TREE      166
Tree, bichromatic      185
Tree, root of      167
Tree, rooted      12 167
Tree, unrooted      167
Truncation      6
TYPE      109
Unit element      7
Unitary polynomial      146
Vandermonde relation      110
Vector      10
Vertex      4 11 165
Vertex, degree of      166
Vertex, distance between      166
Vertex, end      166 178
Vertex, isolated      166
Walk      167
Zeta function      143
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