Walk through combinatorics : An introduction to enumeration and graph theory

By: Bona, MiklosMaterial type: TextTextLanguage: English Publication details: New Jersey World Scientific 2024Edition: 5th edDescription: xxi, 613pISBN: 9798886130836 (PB)Subject(s): Discrete Mathematics | Combinatorics | Graph Theory | Combinatorial Analysis | Mathematics
Contents:
1. Seven Is More Than Six. The Pigeon-Hole Principle 2. One Step at a Time. The Method of Mathematical Induction 3. There are a Lot of Them. Elementary Counting Problems 4. No Matter How You Slice It. The Binomial Theorem and Related Identities 5. Divide and Conquer. Partitions 6. Not So Vicious Cycles. Cycles in Permutations 7. You Shall Not Overcount. The Sieve 8. A Function is Worth Many Numbers. Generating Functions 9. Dots and Lines. The Origins of Graph Theory 10. Staying Connected. Trees 11. Finding A Good Match. Coloring and Matching 12. Do Not Cross. Planar Graphs 13. Does it Clique? Ramsey Theory 14. So Hard To Avoid. Subsequence Conditions on Permutations 15. Who Knows What it Looks Like, But it Exists. The Probabilistic Method 16. At Least Some Order. Partial Orders and Lattices 17. As Evenly As Possible. Block Designs and Error Correcting Codes 18. Are They Really Different? Counting Unlabeled Structures 19. The Sooner The Better. Combinatorial Algorithms 20. Does Many Mean More Than One? Computational Complexity
Summary: The first half of the book walks the reader through methods of counting, both direct elementary methods and the more advanced method of generating functions. Then, in the second half of the book, the reader learns how to apply these methods to fascinating objects, such as graphs, designs, random variables, partially ordered sets, and algorithms. In short, the first half emphasizes depth by discussing counting methods at length; the second half aims for breadth, by showing how numerous the applications of our methods are. New to this fifth edition of A Walk Through Combinatorics is the addition of Instant Check exercises — more than a hundred in total — which are located at the end of most subsections. As was the case for all previous editions, the exercises sometimes contain new material that was not discussed in the text, allowing instructors to spend more time on a given topic if they wish to do so. With a thorough introduction into enumeration and graph theory, as well as a chapter on permutation patterns (not often covered in other textbooks), this book is well suited for any undergraduate introductory combinatorics class.
Item type: BOOKS List(s) this item appears in: New Arrivals (01 June, 2024)
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Includes Bibliography (603-606) and Index

1. Seven Is More Than Six. The Pigeon-Hole Principle
2. One Step at a Time. The Method of Mathematical Induction
3. There are a Lot of Them. Elementary Counting Problems
4. No Matter How You Slice It. The Binomial Theorem and Related Identities
5. Divide and Conquer. Partitions
6. Not So Vicious Cycles. Cycles in Permutations
7. You Shall Not Overcount. The Sieve
8. A Function is Worth Many Numbers. Generating Functions
9. Dots and Lines. The Origins of Graph Theory
10. Staying Connected. Trees
11. Finding A Good Match. Coloring and Matching
12. Do Not Cross. Planar Graphs
13. Does it Clique? Ramsey Theory
14. So Hard To Avoid. Subsequence Conditions on Permutations
15. Who Knows What it Looks Like, But it Exists. The Probabilistic Method
16. At Least Some Order. Partial Orders and Lattices
17. As Evenly As Possible. Block Designs and Error Correcting Codes
18. Are They Really Different? Counting Unlabeled Structures
19. The Sooner The Better. Combinatorial Algorithms
20. Does Many Mean More Than One? Computational Complexity

The first half of the book walks the reader through methods of counting, both direct elementary methods and the more advanced method of generating functions. Then, in the second half of the book, the reader learns how to apply these methods to fascinating objects, such as graphs, designs, random variables, partially ordered sets, and algorithms. In short, the first half emphasizes depth by discussing counting methods at length; the second half aims for breadth, by showing how numerous the applications of our methods are.

New to this fifth edition of A Walk Through Combinatorics is the addition of Instant Check exercises — more than a hundred in total — which are located at the end of most subsections. As was the case for all previous editions, the exercises sometimes contain new material that was not discussed in the text, allowing instructors to spend more time on a given topic if they wish to do so. With a thorough introduction into enumeration and graph theory, as well as a chapter on permutation patterns (not often covered in other textbooks), this book is well suited for any undergraduate introductory combinatorics class.

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