Introduction to Combinatorics 2nd Edition by Martin J Erickson ISBN 1118637534 9781118637531
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Product details:
ISBN 10: 1118637534
ISBN 13: 9781118637531
Author: Martin J. Erickson
“This excellent text should prove a useful accoutrement for any developing mathematics program . . . it’s short, it’s sweet, it’s beautifully written.” —The Mathematical Intelligencer
“Erickson has prepared an exemplary work . . . strongly recommended for inclusion in undergraduate-level library collections.” —Choice
Featuring a modern approach, Introduction to Combinatorics, Second Edition illustrates the applicability of combinatorial methods and discusses topics that are not typically addressed in literature, such as Alcuin’s sequence, Rook paths, and Leech’s lattice. The book also presents fundamental results, discusses interconnection and problem-solving techniques, and collects and disseminates open problems that raise questions and observations.
Many important combinatorial methods are revisited and repeated several times throughout the book in exercises, examples, theorems, and proofs alike, allowing readers to build confidence and reinforce their understanding of complex material. In addition, the author successfully guides readers step-by-step through three major achievements of combinatorics: Van der Waerden’s theorem on arithmetic progressions, Pólya’s graph enumeration formula, and Leech’s 24-dimensional lattice. Along with updated tables and references that reflect recent advances in various areas, such as error-correcting codes and combinatorial designs, the Second Edition also features:
- Many new exercises to help readers understand and apply combinatorial techniques and ideas
- A deeper, investigative study of combinatorics through exercises requiring the use of computer programs
- Over fifty new examples, ranging in level from routine to advanced, that illustrate important combinatorial concepts
- Basic principles and theories in combinatorics as well as new and innovative results in the field
Introduction to Combinatorics, Second Edition is an ideal textbook for a one- or two-semester sequence in combinatorics, graph theory, and discrete mathematics at the upper-undergraduate level. The book is also an excellent reference for anyone interested in the various applications of elementary combinatorics.
Table of contents:
Chapter 1. Basic Counting Methods
1.1 The multiplication principle
1.2 Permutations
1.3 Combinations
1.4 Binomial coefficient identities
1.5 Distributions
1.6 The principle of inclusion and exclusion
1.7 Fibonacci numbers
1.8 Linear recurrence relations
1.9 Special recurrence relations
1.10 Counting and number theory
Notes
Chapter 2. Generating Functions
2.1 Rational generating functions
2.2 Special generating functions
2.3 Partition numbers
2.4 Labeled and unlabeled sets
2.5 Counting with symmetry
2.6 Cycle indexes
2.7 Pólya’s theorem
2.8 The number of graphs
2.9 Symmetries in domain and range
2.10 Asymmetric graphs
Notes
Chapter 3. The Pigeonhole Principle
3.1 Simple examples
3.2 Lattice points, the Gitterpunktproblem, and SET®
3.3 Graphs
3.4 Colorings of the plane
3.5 Sequences and partial orders
3.6 Subsets
Notes
Chapter 4. Ramsey Theory
4.1 Ramsey’s theorem
4.2 Generalizations of Ramsey’s theorem
4.3 Ramsey numbers, bounds, and asymptotics
4.4 The probabilistic method
4.5 Sums
4.6 Van der Waerden’s theorem
Notes
Chapter 5. Codes
5.1 Binary codes
5.2 Perfect codes
5.3 Hamming codes
5.4 The Fano Configuration
Notes
Chapter 6. Designs
6.1 t-designs
6.2 Block designs
6.3 Projective planes
6.4 Latin squares
6.5 MOLS and OODs
6.6 Hadamard matrices
6.7 The Golay code and S(5, 8, 24)
6.8 Lattices and sphere packings
6.9 Leech’s lattice
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