Complement from Permutation

Each entry replaced by n + 1 minus itself.

Permutation → Permutationinvolution

Called as CombinatorialMap(x, "Complement"). The head's page has its examples.

Live

FindStat Mp00069

complement

Matched by value: our map agrees with FindStat's image on each of the 873 rows of size at most 6 we can read (0 unread; its table has 1200 rows).

BijectionGraded mapInvolutionas FindStat records them, checked by FindStat's contributors.

Sents a permutation to its complement.

Object	Image
[1]	[1]
[1,2]	[2,1]
[2,1]	[1,2]
[1,2,3]	[3,2,1]

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00069 has the rest.