Combinatorics

Combinatorics is the study of counting. Different kinds of counting problems can be approached by a variety of techniques.

Introductory Topics

The following topics help shape an introduction to counting techniques:

• Correspondence
• Venn diagram
• Combinations
• Permutations
• Overcounting
• Complementary counting
• Casework
• Constructive counting
• Committee forming
• Pascal's Triangle
• Combinatorial identities
• Binomial Theorem

Intermediate Topics

• Principle of Inclusion-Exclusion
• Conditional Probability
• Recursion
• Correspondence
• Generating functions
• Partitions
• Geometric probability

Olympiad Topics

• Combinatorial geometry
• Graph theory
• Stirling numbers
• Ramsey numbers
• Catalan Numbers
• Counting in two ways

Resources

Listed below are various combinatorics resources including books, classes, and websites.

Books

• Introductory
  • the Art of Problem Solving Introduction to Counting and Probability by David Patrick (details)

See also

• Probability