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Bóna M. — A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory
Bóna M. — A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory

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Название: A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory

Автор: Bóna M.

Аннотация:

This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first edition, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible for the talented and hard-working undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, and algorithms and complexity. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 2006

Количество страниц: 481

Добавлена в каталог: 24.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$BIGSUBSETSUM$      454
$B_{n}$      376
$EVEN$($m$)      117
$HAMCYC$      445
$HAMPATH$      450
$n!$      38
$p$($n$)      94
$p_{k}$($n$)      94
$SAT$      448
$SAT$, $2SAT$      449
$SAT$, $3SAT$      448
$SQ$($n$)      122
$TAUT$      454
$UST$      452
$[N]$      23
$\binom{n}{k}$      44
$\mathbf{l}$      452
$\mathbf{NL}$      452
$\mathbf{NP}$      437
$\mathbf{NP}$-complete      189 446
$\mathbf{PSPACE}$      450
$\mathdf{P}$      436
$\phi$($n$)      138
Acyclic function      226
Adjacency matrix      218
Anti-automorphism      395
Antichain      378
ascent      325
atom      398
Augmenting path      253
Automorphism      196
Bayes’ Theorem      354 356
Bell numbers      93
Bijection      41
Binet — Cauchy formula      221
Binomial coefficients      44
Binomial coefficients, for a real exponent      73
Binomial theorem      65
Binomial theorem, for a real exponent      73
Bipartite graphs      243
Bipartite graphs, complete      200 213 245
Boolean algebra      376
Boolean expression      447
BREADTH FIRST SEARCH      425
Brooks theorem      256
Bubblesort      409
Canonical cycle form      111
Catalan numbers      179 311
Cayley’s formula      211
Center of a graph      228
Chain      376
Chain cover      379
Chain, length of      382
Chromatic number      242
Chromatic polynomial      259 260
CLIQUE      288
Coatom      398
Complement in a lattice      395
Complement of a graph      228
Complement of a permutation      126 312
Complement of a set      44
Complete graph      191
Complete graph, $k$-partite      254
Composition of an integer      89
Composition of an integer, weak composition      89
Compositional formula for exponential gen. functions      166
Compositional formula for ordinary gen. functions      159
Conjunctive normal form      447
Connected components      185
Connected graph      185
Connected graph, strongly      191
CONp      440
Cook’s theorem      448
Covering matrix      395
Covering relation      371
cube      277
Cycles in graphs      188
Cycles in permutations      110
Decreasing binary tree      323
Degree of a vertex      184
Depth first search      425
Derangements      135
Descent      138 325
Diameter of a graph      232
Dijkstra algorithm      421
Dilworth’s theorem      379
Dimension of a poset      395
Direct product of posets      382
Directed graph      190
Distance in a graph      228
Distribution problems      89
Distributive lattice      395
dodecahedron      278
Dominance order      398
Dual of a planar graph      276
Durfee-square      101
Edge-cover      262
Erd$\ddot{o}$s — Szekeres theorem      294
Eulerian walk      185
Eulerian walk, closed      185
Euler’s theorem on planar graphs      270
Event      346
Excedance      138
Expectation      355
Expectation, conditional      361
Expectation, linearity of      357
Exponential formula      165
Exponential formula, permutation version      170
Factor-critical      261
Factorial      38
Ferrers shape      95
Fibonacci number      173
Fixed point      110 122
Fixed point, fixed point-free      134
Forest      210
Forest, rooted      213
Formal power series      147
Four-color theorem      281
Gap position      119
Generating function, composition of      157 164
Generating function, exponential      160
Generating function, ordinary      146
Generating function, products of      152 162
Graph      184
Graph, bipartite      243
Graph, connected      185
Graph, directed      190
Graph, minimally connected      207
Graph, planar      270
Graph, regular      197
Graph, simple      185
Graphical partition      198
Greedy algorithm      214
Hall’s theorem      251
Halting problem      408
Hamiltonian cycle      188 439
Hamiltonian path      188
Hasse diagram      377
Hypercube      200
icosahedron      278
Ideal      375
Ideal, principal      375
Immermann — Szelepcs$\acute{e}$nyi theorem      452
In-degree      191
In-order      324
Incidence algebra      381
Incidency matrix      221
Inclusion-Exclusion Principle      138
Incomparable elements      376
Indecomposable permutation      169
INDEPENDENT - SET$      454
Independent events      351 355
Independent set of edges      248
Indicator variable      359
Induced subgraph      196
Induction, strong      24
Induction, weak      19
Injection      41
Input      408
Interval order      398
Interval order, unit      398
Inverse of a permutation      121
inversion      123
Involution      121
Isomorphism of graphs      194
Join      389
K$\ddot{o}$nig’s theorem      262
Kruskal algorithm      217 417
Kuratowski’s Theorem      272
Laplacian      224
Lattice      388
Leaf      210
Left-to-right maximum      126
Left-to-right minimum      313
Linear extension      380
Literal      447
Locally finite poset      381
Log-concave sequence      76
Lonely permutation      327
Loop      185
M$\ddot{o}$bius function      383
M$\ddot{o}$bius inversion formula      387
M$\ddot{o}$bius matrix      383
Magic square      50 260
Matching      250
Matching, maximum, maximal      252
Matching, perfect      248
Matrix-tree theorem      222
Matrix-tree theorem, eigenvalue version      224
Maximum and maximal elements      377
Meet      389
Meet-semilattice      390
Mergesort      412
Modular lattice      395
Motzkin numbers      168
Multinomial coefficients      71
Multinomial theorem      70 72
Multiset      23 39
Mutually exclusive events      347
Nonconstructive proofs      348
Noncrossing partitions      330
Northeastern lattice paths      76
Octahedrite      282
octahedron      278
ODD($m$)      117
One-line notation      111
Order polynomial      397
Ordered degree-sequence      198
Out-degree      191
Output      408
Parking function      226
Partial fraction decomposition      148
Partially ordered set      375
Partitions of a set      91
Partitions of a set, formula for the number of      136
Partitions of a set, noncrossing      325
Partitions of a set, type of      98
Partitions of an integer      94
Partitions of an integer, asymptotic formula      95
Partitions of an integer, conjugate      95
Partitions of an integer, self-conjugate      95
Pascal triangle      67
Path      185
Pattern avoidance      307
Peak      362
permutations      37
Permutations, alternating      169
Permutations, even      122
Permutations, indecomposable      169
Permutations, matrix of      121
Permutations, odd      122
Permutations, of a multiset      40
Permutations, roots of      122
Permutations, stack sortable      319
Permutations, two-stack sortable      321
Permutations, type of      113
Permutations, with restricted cycles      116
Petersen graph      198
Pigeon-hole principle      1 3
Polyhedron      272
Polyhedron, trivalent      282
POSET      370
Postorder      324
Pr$\ddot{u}$fer code      226
Pratt’s theorem      441
PRIMES$      440
Prim’s algorithm      431
probability      345
Probability, conditional      351
Product formula for ex      163
Product formula for ord. gen. functions      152
Ramsey number      290
Ramsey theorem      289
Random variable      356
Random variable, independent      357
Reachability      452
Refinement order      377
Refining sequence      227
Reflection principle      85
Regular polyhedra      269
Right-to-left maximum      314
Rooted forest      210
Roots of a permutation      121
Run      362
Sample space      346
Saturated non-factorizable      257
Schr$\ddot{o}$der numbers      169
Self-dual poset      395
Semi-factorial      73
Set      22
Sieve formula      132
Simpson’s paradox      353
Spanning tree      214
Spanning tree, minimum weight      217
Sperner’s lemma      283
Stack-sorting      319
Standard deviation      365
Stanley — Wilf conjecture      311
Stirling numbers of the first kind      113
Stirling numbers of the second kind      91
Stirling’s formula      38
Strings over a finite alphabet, with no repetitions allowed      43
Strings over a finite alphabet, with repetitions allowed      40
Subgraph      196
Subgraph, induced      196
SUBSETSUM$      450
Superpattern      332
Surjection      41
Surjection, number of      92
Symmetric difference      208
Symmetric group      112
tetrahedron      277
Three houses, three wells      270
Tournament      191
Tournament, transitive      192
Trace      127
Transition lemma      115
TREE      209
Tree, complete $k$-ary      226
Tree, decreasing binary      323
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