Editing Combinatorial principles (section)

{{Short description|Methods used in combinatorics}}
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 combinatorics|enumerative]] purposes. [[Bijective proof]]s are utilized to demonstrate that two sets have the same [[cardinality|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 mathematics|discrete]] context. 

Many [[combinatorial identities]] arise from [[Double counting (proof technique)|double counting]] methods or the [[method of distinguished element]]. [[Generating function]]s and [[recurrence relation]]s are powerful tools that can be used to manipulate sequences, and can describe if not resolve many combinatorial situations.