Difference between revisions of "Combinatorics"
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| − | '''Combinatorics''' is the study of discrete structures in general, and enumeration on discrete structures in particular. For example, the number of three-[[cycle|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]]. | + | '''Combinatorics''' is the study of discrete structures in general, and enumeration on discrete structures in particular. For example, the number of three-[[cycle|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|principle of inclusion-exclusion]]. |
== Student Guides to Combinatorics == | == Student Guides to Combinatorics == | ||
Revision as of 14:43, 12 January 2011
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)
- Undergraduate level
- Generatingfunctionology by Herbert S. Wilf. Free fulltext download here: [1]
