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Introductory Combinatorics (Classic Version) 5th edition [Minkštas viršelis]

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Appropriate for one- or two-semester, junior- to senior-level combinatorics courses.

This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles.


This trusted best-seller covers the key combinatorial ideas–including the pigeon-hole principle, counting techniques, permutations and combinations, Pólya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, combinatortial structures (matchings, designs, graphs), and flows in networks. The 5th Edition incorporates feedback from users to the exposition throughout and adds a wealth of new exercises.

1 What Is Combinatorics?
1(26)
1.1 Example: Perfect Covers of Chessboards
3(4)
1.2 Example: Magic Squares
7(3)
1.3 Example: The Four-Color Problem
10(1)
1.4 Example: The Problem of the 36 Officers
11(3)
1.5 Example: Shortest-Route Problem
14(1)
1.6 Example: Mutually Overlapping Circles
15(2)
1.7 Example: The Game of Nim
17(3)
1.8 Exercises
20(7)
2 Permutations and Combinations
27(42)
2.1 Four Basic Counting Principles
27(8)
2.2 Permutations of Sets
35(6)
2.3 Combinations (Subsets) of Sets
41(5)
2.4 Permutations of Multisets
46(6)
2.5 Combinations of Multisets
52(4)
2.6 Finite Probability
56(4)
2.7 Exercises
60(9)
3 The Pigeonhole Principle
69(18)
3.1 Pigeonhole Principle: Simple Form
69(4)
3.2 Pigeonhole Principle: Strong Form
73(4)
3.3 A Theorem of Ramsey
77(5)
3.4 Exercises
82(5)
4 Generating Permutations and Combinations
87(40)
4.1 Generating Permutations
87(6)
4.2 Inversions in Permutations
93(5)
4.3 Generating Combinations
98(11)
4.4 Generating r-Subsets
109(4)
4.5 Partial Orders and Equivalence Relations
113(5)
4.6 Exercises
118(9)
5 The Binomial Coefficients
127(34)
5.1 Pascal's Triangle
127(3)
5.2 The Binomial Theorem
130(9)
5.3 Unimodality of Binomial Coefficients
139(4)
5.4 The Multinomial Theorem
143(3)
5.5 Newton's Binomial Theorem
146(3)
5.6 More on Partially Ordered Sets
149(5)
5.7 Exercises
154(7)
6 The Inclusion--Exclusion Principle and Applications
161(44)
6.1 The Inclusion--Exclusion Principle
161(7)
6.2 Combinations with Repetition
168(4)
6.3 Derangements
172(5)
6.4 Permutations with Forbidden Positions
177(4)
6.5 Another Forbidden Position Problem
181(2)
6.6 Mobius Inversion
183(15)
6.7 Exercises
198(7)
7 Recurrence Relations and Generating Functions
205(60)
7.1 Some Number Sequences
206(9)
7.2 Generating Functions
215(7)
7.3 Exponential Generating Functions
222(6)
7.4 Solving Linear Homogeneous Recurrence Relations
228(17)
7.5 Nonhomogeneous Recurrence Relations
245(8)
7.6 A Geometry Example
253(4)
7.7 Exercises
257(8)
8 Special Counting Sequences
265(56)
8.1 Catalan Numbers
265(9)
8.2 Difference Sequences and Stirling Numbers
274(17)
8.3 Partition Numbers
291(7)
8.4 A Geometric Problem
298(3)
8.5 Lattice Paths and Schroder Numbers
301(14)
8.6 Exercises
315(6)
9 Systems of Distinct Representatives
321(20)
9.1 General Problem Formulation
322(4)
9.2 Existence of SDRs
326(4)
9.3 Stable Marriages
330(7)
9.4 Exercises
337(4)
10 Combinatorial Designs
341(54)
10.1 Modular Arithmetic
341(12)
10.2 Block Designs
353(9)
10.3 Steiner Triple Systems
362(6)
10.4 Latin Squares
368(20)
10.5 Exercises
388(7)
11 Introduction to Graph Theory
395(66)
11.1 Basic Properties
396(10)
11.2 Eulerian Trails
406(8)
11.3 Hamilton Paths and Cycles
414(5)
11.4 Bipartite Multigraphs
419(7)
11.5 Trees
426(6)
11.6 The Shannon Switching Game
432(6)
11.7 More on Trees
438(11)
11.8 Exercises
449(12)
12 More on Graph Theory
461(44)
12.1 Chromatic Number
462(10)
12.2 Plane and Planar Graphs
472(4)
12.3 A Five-Color Theorem
476(4)
12.4 Independence Number and Clique Number
480(8)
12.5 Matching Number
488(5)
12.6 Connectivity
493(5)
12.7 Exercises
498(7)
13 Digraphs and Networks
505(36)
13.1 Digraphs
505(11)
13.2 Networks
516(7)
13.3 Matchings in Bipartite Graphs Revisited
523(10)
13.4 Exercises
533(8)
14 Polya Counting
541
14.1 Permutation and Symmetry Groups
542(10)
14.2 Burnside's Theorem
552(7)
14.3 Polya's Counting Formula
559(17)
14.4 Exercises
576
About our author Richard A. Brualdi is Bascom Professor of Mathematics, Emeritus at the University of Wisconsin - Madison. He served as Chair of the Department of Mathematics from 1993-1999. His research interests lie in matrix theory and combinatorics/graph theory. Professor Brualdi is the author or co-author of 6 books, and has published extensively. He is one of the editors-in-chief of the journal "Linear Algebra and its Applications" and of the journal "Electronic Journal of Combinatorics." He is a member of the American Mathematical Society, the Mathematical Association of America, the International Linear Algebra Society, and the Institute for Combinatorics and its Applications. He is also a Fellow of the Society for Industrial and Applied Mathematics.