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

Miklós Bóna
Publisher: 
World Scientific
Publication Date: 
2011
Number of Pages: 
546
Format: 
Hardcover
Edition: 
3
Price: 
110.00
ISBN: 
9789814335232
Category: 
Textbook
BLL Rating: 

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Fernando Gouvêa
, on
07/12/2011
]

See Christopher Hanusa's review of the second edition. In addition to the usual corrections, the third edition has two new chapters: chapter 17, "As Evenly As Possible: Block Designs and Error Correcting Codes" and chapter 18, "Are They Really Different: Counting Unlabeled Structures". Bóna's Walk remains one of the best introductory textbooks in the field.

  • Basic Methods
    • Seven is More Than Six. The Pigeon-Hole Principle
    • One Step at a Time. The Method of Mathematical Induction
  • Enumerative Combinatorics
    • There are a Lot of Them. Elementary Counting Problems
    • No Matter How You Slice It. The Binomial Theorem and Related Identities
    • Divide and Conquer. Partitions
    • Not So Vicious Cycles. Cycles in Permutations
    • You Shall Not Overcount. The Sieve
    • A Function is Worth Many Numbers. Generating Functions
  • Graph Theory
    • Dots and Lines. The Origins of Graph Theory
    • Staying Connected. Trees
    • Finding a Good Match. Coloring and Matching
    • Do Not Cross. Planar Graphs
  • Horizons
    • Does It clique? Ramsey Theory
    • So Hard to Avoid. Subsequence Conditions on Permutations
    • Who Knows What It Looks Like, But It Exists. The Probabilistic Method
    • At Least Some Order. Partial Orders and Lattices
    • As Evenly as Possible. Block Designs and Error Correcting Codes
    • Are They Really Different? Counting Unlabeled Structures
    • The Sooner the Better. Combinatorial Algorithms
    • Does Many Mean More Than One? Computational Complexity

 

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