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