Difference between revisions of "Combinatorial principles"
Karl Jones (Talk | contribs) (Created page with "In proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used. The rule of sum, rule of product, and...") |
Karl Jones (Talk | contribs) |
||
| Line 1: | Line 1: | ||
In proving results in [[combinatorics]] several useful combinatorial rules or combinatorial principles are commonly recognized and used. | In proving results in [[combinatorics]] several useful combinatorial rules or combinatorial principles are commonly recognized and used. | ||
| − | The rule of sum, rule of product, and inclusion–exclusion principle are often used for enumerative purposes. Bijective proofs are utilized to demonstrate that two sets have the same number of elements. The pigeonhole principle often ascertains the existence of something or is used to determine the minimum or maximum number of something in a discrete context. | + | The [[rule of sum]], [[rule of product]], and inclusion–exclusion principle are often used for [[Enumerative combinatorics|enumerative]] purposes. |
| + | |||
| + | Bijective proofs are utilized to demonstrate that two sets have the same number of elements. | ||
| + | |||
| + | The [[pigeonhole principle]] often ascertains the existence of something or is used to determine the minimum or maximum number of something in a discrete context. | ||
Many combinatorial identities arise from double counting methods or the method of distinguished element. | Many combinatorial identities arise from double counting methods or the method of distinguished element. | ||
| Line 10: | Line 14: | ||
* [[Combinatorics]] | * [[Combinatorics]] | ||
| + | * [[Enumerative combinatorics]] | ||
== External links == | == External links == | ||
| − | * [ Combinatorial principles] @ Wikipedia | + | * [https://en.wikipedia.org/wiki/Combinatorial_principles Combinatorial principles] @ Wikipedia |
[[Category:Combinatorics]] | [[Category:Combinatorics]] | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Latest revision as of 13:33, 4 April 2017
In proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used.
The rule of sum, rule of product, and inclusion–exclusion principle are often used for enumerative purposes.
Bijective proofs are utilized to demonstrate that two sets have the same number of elements.
The pigeonhole principle often ascertains the existence of something or is used to determine the minimum or maximum number of something in a discrete context.
Many combinatorial identities arise from double counting methods or the method of distinguished element.
Generating functions and recurrence relations are powerful tools that can be used to manipulate sequences, and can describe if not resolve many combinatorial situations.
See also
External links
- Combinatorial principles @ Wikipedia
