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A walk through combinatorics. An introduction to enumeration and graph theory

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Author(s): Stanley, Richard P.; Bóna, Miklós
Edition: 3rd ed., reprinted
Publisher: World Scientific
Year: 2011

Language: English
Pages: 550
City: New Jersey
Tags: matematika -- kombinatorika -- preštevanja -- teorija grafov -- Ramseyeva teorija -- delna urejenost -- algoritmi -- naloge -- rešitve;mathematics -- combinatorics -- enumeration -- graph theory -- Ramsey theory -- partial orders -- combinatorial algorithms -- computational complexity -- exercises -- solutions

Content: 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.