There are 57 maps with codomain Permutations in the database:
(and possibly some waiting for verification)
injective
graded
bijective
surjective
involutive
idempotent
Number of maps: 329
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Alternating sign matricesAlternating sign matricesDyck pathsPerfect matchingsPermutationsSemistandard tableauxBinary treesBinary treesGraphsOrdered treesPosetsBinary wordsBinary wordsInteger compositionsCoresInteger partitionsDecorated permutationsDyck pathsSet partitionsSkew partitionsStandard tableauxFinite Cartan typesGelfand-Tsetlin patternsGelfand-Tsetlin patternsGraphsLatticesInteger compositionsInteger partitionsLatticesOrdered set partitionsOrdered set partitionsOrdered treesParking functionsParking functionsPerfect matchingsPermutationsSigned permutationsPlane partitionsPlane partitionsPosetsSemistandard tableauxSet partitionsSigned permutationsSkew partitionsStandard tableaux
Alternating sign matricesBinary treesDecorated permutationsDyck pathsOrdered set partitionsParking functionsPerfect matchingsPermutationsSemistandard tableauxSet partitionsSigned permutationsStandard tableauxPermutationsto left key permutationto 132-avoiding permutationto 312-avoiding permutationpermutationlower permutationupper permutationto 321-avoiding permutation (Krattenthaler)to 321-avoiding permutation (Billey-Jockusch-Stanley)Ringelto non-crossing permutationto 321-avoiding permutationto 132-avoiding permutationto 312-avoiding permutationto permutationto car permutationto labelling permutationnon-nesting-exceedence permutationto permutationcactus evacuationLehmer code rotationDemazure product with inverseinverse Foata bijectionrunsortdescent views to invisible inversion bottomsClarke-Steingrimsson-Zeng inversedescent views to invisible inversion bottomsClarke-Steingrimsson-ZengCorteelinvert Laguerre heaprestrictionInverse fireworks mapAlexandersson Kebedeconjugation by long cyclecatalanizationBackward Rotationinverse toric promotiontoric promotionones to leadingweak order rowmotionTanimotoLehmer-code to major-code bijectionreverseinverseFoata bijectionSimion-Schmidt mapcomplementmajor-index to inversion-number bijectionfirst fundamental transformationinverse first fundamental transformationKreweras complementInverse Kreweras complementcycle-as-one-line notationreading word permutationto permutationpermutationstandardizereading word permutation