Combinatorics

Combinatorics is the study of discrete structures in general and enumeration on discrete structures in particular. For example, the number of three-cycles in a given graph is a combinatoric problem, as is the derivation of an analytic solution to the Fibonacci recurrence, and so too methods of solving the Rubiks cube. Different kinds of counting problems can be approached by a variety of techniques, such as generating functions or the inclusion-exclusion principle.

Student Guides to Combinatorics

• Introductory topics in combinatorics
• Intermediate topics in combinatorics
• Olympiad topics in combinatorics

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)
• Intermediate & Beyond
  • the Art of Problem Solving Intermediate Counting and Probability by David Patrick (details)
• Undergraduate level
  • Generatingfunctionology by Herbert S. Wilf. Free fulltext download here: [1]

See also

• Probability
• Introductory Problems
• Intermediate Problems
• Olympiad Problems