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 a non-recursive formula for the Fibonacci numbers, 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 principle of inclusion-exclusion.

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)
  • "Combinatorics:A Guided Tour" by David R. Mazur.Follow this (link)
• Undergraduate level
  • Generatingfunctionology by Herbert S. Wilf. Free fulltext download here: [1]

See also

• Probability
• Introductory Problems
• Intermediate Problems
• Olympiad Problems