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}}.</ref> Since their paper, many other bijections have been given, see {{harvtxt|Claesson|Kitaev|2008}} for a survey.<ref>{{Citation| last1=Claesson | first1=Anders| last2=Kitaev | first2=Sergey| arxiv = 0805.1325| title=Classification of bijections between 321- and 132-avoiding permutations| year=2008| journal=[[Séminaire Lotharingien de Combinatoire]]| url = http://www.emis.ams.org/journals/SLC/wpapers/s60claekit.pdf| volume=60| pages=B60d| mr = 2465405| bibcode=2008arXiv0805.1325C}}.</ref>
In general, if |''Av<sub>n</sub>''(β)| = |''Av<sub>n</sub>''(σ)| for all ''n'', then β and σ are said to be [[Wilf equivalence|''Wilf-equivalent'']]. Many Wilf-equivalences stem from the trivial fact that |''Av<sub>n</sub>''(β)| = |''Av<sub>n</sub>''(''β''<sup>−1</sup>)| = |''Av<sub>n</sub>''(β<sup>rev</sup>)| for all ''n'', where β<sup>''-1''</sup> denotes the [[Permutation#Product and inverse|inverse]] of β and β<sup>rev</sup> denotes the reverse of β. (These two operations generate the [[Examples of groups#The symmetry group of a square - dihedral group of order 8|Dihedral group D<sub>8</sub>]] with a natural action on [[permutation matrices]].) However, there are also numerous examples of nontrivial Wilf-equivalences (such as that between ''123'' and ''231''):
* {{harvtxt|Stankova|1994}} proved that the permutations 1342 and 2413 are Wilf-equivalent.<ref>{{Citation | last1=Stankova | first1=Zvezdelina | title=Forbidden subsequences | mr = 1297387 | year=1994 | journal=[[Discrete Mathematics (journal)|Discrete Mathematics]] | volume=132 | issue=1–3 | pages=291–316 | doi = 10.1016/0012-365X(94)90242-9}}.</ref>
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