Difference between revisions of "Combinatorics"
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| − | '''Combinatorics''' is the study of | + | '''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 [[analysis|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 == | == Student Guides to Combinatorics == | ||
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* Intermediate & Beyond | * Intermediate & Beyond | ||
** ''the Art of Problem Solving Intermediate Counting and Probability'' by David Patrick [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?item_id=302 (details)] | ** ''the Art of Problem Solving Intermediate Counting and Probability'' by David Patrick [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?item_id=302 (details)] | ||
| + | * Undergraduate level | ||
| + | ** ''Generatingfunctionology'' by Herbert S. Wilf. Free fulltext download here: [http://www.math.upenn.edu/~wilf/DownldGF.html] | ||
== See also == | == See also == | ||
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* [[:Category:Intermediate Combinatorics Problems|Intermediate Problems]] | * [[:Category:Intermediate Combinatorics Problems|Intermediate Problems]] | ||
* [[:Category:Olympiad Combinatorics Problems|Olympiad Problems]] | * [[:Category:Olympiad Combinatorics Problems|Olympiad Problems]] | ||
| − | [[Category:Combinatorics]] | + | [[Category:Combinatorics]] [[Category:Mathematics]] |
Revision as of 20:32, 13 June 2008
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]
