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Introductory Combinatorics

Edition: 
3
Publisher: 
Brooks Cole
Number of Pages: 
654
Price: 
152.95
ISBN: 
0121108309
Date Received: 
Friday, July 21, 2006
Reviewable: 
Yes
Include In BLL Rating: 
Yes
Kenneth P. Bogart
Publication Date: 
2000
Format: 
Hardcover
Audience: 
Category: 
Textbook
BLL Committee
07/27/2010
BLL Rating: 

 1. AN INTRODUCTION TO ENUMERATION.
Elementary Counting Principles. Functions and the Pigeonhole Principle. Subsets. Using Binomial Coefficients. Mathematical Induction.
2. EQUIVALENCE, RELATIONS, PARTITIONS, AND MULTISETS.
Equivalence Relations. Distributions and Multisets. Partitions and Stirling Numbers. Partitions of Integers.
3. ALGEBRAIC COUNTING TECHNIQUES.
The Principle of Inclusion and Exclusion. The Concept of a Generating Function. Applications to Partitions and Inclusion--Exclusion. Recurrence Relations and Generating Functions. Exponential Generating Functions.
4. GRAPH THEORY.
Eulerian Walks and the Idea of Graphs. Trees. Shortest Paths and Search Trees. Isomorphism and Planarity. Digraphs. Coloring. Graphs and Matrices.
5. MATCHING AND OPTIMIZATION.
Matching Theory. The Greedy Algorithm. Network Flows. Flows, Connectivity, and Matching.
6. COMBINATORIAL DESIGNS.
Latin Squares and Graeco-Latin Squares. Block Designs. Construction and Resolvability of Designs. Affine and Projective Planes. Codes and Designs.
7. ORDERED SETS.
Partial Orderings. Linear Extensions and Chains. Lattices. Boolean Algebras. Möbius Functions. Products of Orderings.
8. ENUMERATION UNDER GROUP ACTION.
Permutation Groups. Groups Acting on Sets. Pólya's Enumeration Theorem.

Publish Book: 
Modify Date: 
Tuesday, July 27, 2010

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