Research Catalog

Title

A walk through combinatorics : an introduction to enumeration and graph theory / Miklós Bóna.

Author

Bóna, Miklós.

Publication

Hackensack, NJ : World Scientific Pub., ©2006.

Items in the Library & Off-site

Details

Description

xvii, 469 pages : illustrations; 24 cm

Summary

The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, and algorithms and complexity.

Subject

• Combinatorial analysis
• Kombinatorik
• Graphentheorie
• Abzählen
• Combinatieleer
• Combinatória
• Grafteori
• Kombinatorik

Genre/Form

Einführung.

Bibliography (note)

• Includes bibliographical references (p. 461-463) and index.

Contents

pt. 1. Basic methods -- Seven is more than six. The pigeon-hole principle -- One step at a time. The method of mathematical induction -- pt. 2. 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 -- pt. 3. 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 -- pt. 4. 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 -- The sooner the better. Combinatorial algorithms.

ISBN

• 9812568859
• 9789812568854
• 9812568867
• 9789812568861

LCCN

2006048235

OCLC

• ocm69734665
• 69734665
• SCSB-1414735

Owning Institutions

Princeton University Library