Editing Bijective proof (section)

== Other examples ==

Problems that admit bijective proofs are not limited to binomial coefficient identities. As the complexity of the problem increases, a bijective proof can become very sophisticated. This technique is particularly useful in areas of [[discrete mathematics]] such as [[combinatorics]], [[graph theory]], and [[number theory]].

The most classical examples of bijective proofs in combinatorics include:
* [[Prüfer sequence]], giving a proof of [[Cayley's formula]] for the number of [[labeled tree]]s.
* [[Robinson-Schensted algorithm]], giving a proof of [[William Burnside|Burnside]]'s formula for the [[symmetric group]].
* [[Integer_partition#Conjugate_and_self-conjugate_partitions|Conjugation]] of [[Young diagram]]s, giving a proof of a classical result on the number of certain [[integer partition]]s.
* Bijective proofs of the [[pentagonal number theorem]].
* Bijective proofs of the formula for the [[Catalan number]]s.