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
Listed below are various combinatorics resources including books, classes, and websites.
- the Art of Problem Solving Introduction to Counting and Probability by David Patrick (details)
- Generatingfunctionology by Herbert S. Wilf. Free fulltext download here: