There are 27 maps with domain Permutations in the database. There are possibly some more waiting for verification.

Mp00059Permutations ⟶ Standard tableaux
Robinson-Schensted insertion tableau
Mp00060Permutations ⟶ Integer partitions
Robinson-Schensted tableau shape
Mp00061Permutations ⟶ Binary trees
to increasing tree
Mp00062Permutations ⟶ Permutations
Lehmer-code to major-code bijection
Mp00063Permutations ⟶ Alternating sign matrices
to alternating sign matrix
Mp00064Permutations ⟶ Permutations
Mp00065Permutations ⟶ Posets
permutation poset
Mp00066Permutations ⟶ Permutations
Mp00067Permutations ⟶ Permutations
Foata bijection
Mp00068Permutations ⟶ Permutations
Simion-Schmidt map
Mp00069Permutations ⟶ Permutations
Mp00070Permutations ⟶ Standard tableaux
Robinson-Schensted recording tableau
Mp00071Permutations ⟶ Integer compositions
descent composition
Mp00072Permutations ⟶ Binary trees
binary search tree: left to right
Mp00073Permutations ⟶ Permutations
major-index to inversion-number bijection
Mp00086Permutations ⟶ Permutations
first fundamental transformation
Mp00087Permutations ⟶ Permutations
inverse first fundamental transformation
Mp00088Permutations ⟶ Permutations
Kreweras complement
Mp00089Permutations ⟶ Permutations
Inverse Kreweras complement
Mp00090Permutations ⟶ Permutations
cycle-as-one-line notation
Mp00108Permutations ⟶ Integer partitions
cycle type
Mp00109Permutations ⟶ Binary words
descent word
Mp00114Permutations ⟶ Binary words
connectivity set
Mp00126Permutations ⟶ Permutations
cactus evacuation
Mp00127Permutations ⟶ Dyck paths
left-to-right-maxima to Dyck path
Mp00130Permutations ⟶ Binary words
descent tops
Mp00131Permutations ⟶ Binary words
descent bottoms