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Šimša J., Kucčra R., Herman J. — Counting and Configurations: Problems in Combinatorics, Arithmetic, and Geometry
&#352im&#353a J., Kuc&#269ra R., Herman J. — Counting and Configurations: Problems in Combinatorics, Arithmetic, and Geometry



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Название: Counting and Configurations: Problems in Combinatorics, Arithmetic, and Geometry

Авторы: Šimša J., Kucčra R., Herman J.

Аннотация:

This book presents methods of solving problems in three areas of elementary combinatorial mathematics: classical combinatorics, combinatorial arithmetic, and combinatorial geometry. In each topic, brief theoretical discussions are immediately followed by carefully worked-out examples of increasing degrees of difficulty, and by exercises that range from routine to rather challenging. While this book emphasizes some methods that are not usually covered in beginning university courses, it nevertheless teaches techniques and skills that are useful not only in the specific topics covered here. There are approximately 310 examples and 650 exercises.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 392

Добавлена в каталог: 23.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Addition rule      2
Anagram      18
Antiarithmetic sequence      139
Appel, K.      275
Arithmetic sequence      136
Arrangement      109
Arrangement of n elements      6
Arrangement, with repetitions      17
Array      143
Ascending integer      31
Ascending integer, strictly      32
Attainability problem      193
Auxiliary colorings      281
Balanced partition      180
Bernoulli’s inequality      327
Bezout’s Theorem      351
Bijection      96
Bijection rule      6 56
Binomial coefficient      11
Boundary      242
Cartesian, coordinates      62
Cartesian, product      4
Cayley's problem      230
Checkerboard      269
Chessboard      269
Class of a partition      175
Classical combinatorics      1
Collinear points      220
Coloring      273
Coloring of chessboards      277
Coloring of points      273
Coloring of regions      275
Column sum      143
Combination, with repetitions      20
Combination, without repetitions      11
Combinatorial, geometry      217
Combinatorial, number      11
Combinatorial, planimetry      218
Combinatorial, topology      218
Combinatorics, classical      1
conditions      24
Conditions, bounded region      242
Conditions, Burnside’s lemma      97
Conditions, point      242
Configurations, numerical      107
Connected set      242
Convex, body      219
Convex, hull      219
Convex, polygon      219
Counting, intersections      222
Counting, polygons      230
Counting, triangles      225
Covering      257
Curve      242
Cyclic sequence      122
Decimal system      29
Digit representation      79
Diophantine equation      33
Direct construction      107
Dirichlet's principle      2 5 33 107
Dirichlet’s Theorem      138
Discrete geometry      218
Distributions into bins      76
Dividing space      255
Dividing the plane, with a system of lines      243
Dividing the plane, with closed curves      246
Divisibility      109
dodecahedron      100
Domino      269
Equivalence relation      96
Euler’s $\varphi$-function      86
Extremal problem      108
Fibonacci, numbers      330
Fibonacci, sequence      187
Finite sequence      121
Finiteness problem      193
Fixed point      82
Four-color problem      273
Function, Euler’s      86
Function, Mobius      87 361
Function, onto      75
General position of lines      244
General position of planes      255
Generalized diagonal      154
Geometric sequence      136
Graph      133
Graph, planar      275
Hadwiger, Hugo      218
Haken, W.      275
Hasse diagram      115
Heawood's Theorem      276
Heawood, P.J.      275
Helly's theorem      237
Identity permutation      82
Inclusion-Exclusion Principle      2 66 258
Inclusion-exclusion principle, generalization      89
Infinite sequence      121
Interior point      242
Invariant      196
Iteration      192
Jordan’s Theorem      238
Jung's theorem      260
k-combination      11
Length of a sequence      121
Line bundie      222
Linear ordering      115
Mapping      192
Mathematical induction      107
Matrix      143
Method of auxiliary coloring      281
Method of construction      107
Method of extremes      108 232
Method of invariants      196
Method of parallels      229
Method of words      56
Mobius, function      87 361
Mobius, inversion formula      87
Multiplication rule      2 3
Multiplicity      17
Multiset      16
Newton’s theorem      354
Nonconvex polygon      238
Number of divisors      89
Numerical configurations      107
Onto function      75
Open set      242
Optimization      217
Ordered fc-tuple      1
overlapping      257
Packing      257
Parity-balanced sequence      132
Partially ordered set      115
Partition of a set      174
Partition, cardinality-balanced      180
Partition, sum-balanced      180
Pascal’s triangle      160
Perfect power      139
periodicity      193
Periodicity problem      193
Periodicity, stabilization      193
Permutation      8 82
Pigeonhole      2 5 107
Pigeonhole Principle      2 5 107
Planar graph      275
Polya’s theory of enumeration      95
Polygon      238
Polygon, convex      219
Polygon, nonconvex      238
Principle, Dirichlet’s      2 5 33 107
Principle, inclusion-exclusion      2 66 258
Problem, attainability      193
Problem, Cayley’s      230
Problem, extremal      108
Problem, finiteness      193
Problem, four-color      273
SEQUENCE      121
Sequence, antiarithmetic      139
Sequence, arithmetic      136
Sequence, cyclic      122
Sequence, Fibonacci      187
Sequence, geometric      136
Sequence, infinite      121
Sequence, non decreasing      22
Sequence, parity-balanced      132
Set, open      242
Set, partially ordered      115
Set, partition of      174
Stabilization problem      193
Stirling numbers of the second kind      78
subarray      148
Subgroup      97
Subsequence      127
Subsets II, sum of divisors      89
Sylvester's      232
Sylvester's bijection      6
Sylvester's bounded      242
Sylvester's method      103
Sylvester's multiplication      2 3
Sylvester's Product of divisors      89
Sylvester's Recursive, construction      107
Sylvester's Region      242
Sylvester's Relation      192
Sylvester's Riemann, Bernhard      217
Sylvester's Row sum      143
Sylvester's Rule, addition      2
Sylvester's unbounded      242
Sylvester’s problem      232
Tetromino      269
Thales circle      364
Theorem, Bezout’s      351
Theorem, Dirichlet’s      138
Theorem, Heawood's      276
Theorem, Helly’s      220
Theorem, Jordan's      238
Theorem, Jung’s      260
Theorem, Newton’s      354
Theory of convex sets      218
Tilings      218 257
Triangular array      160
Tromino      269
Unbounded region      242
Valuation      203
van der Waerden’s      174
van der Waerden’s theorem      175
Variation, W      0
Walks in rectangular grids      62
With repetitions      13
Without repetitions      8
Without repetitions, vertex of a polygon      220
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