There are 57 maps with domain 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
PermutationsAlternating sign matricesBinary treesBinary wordsDyck pathsGraphsInteger compositionsInteger partitionsLatticesParking functionsPermutationsPosetsSet partitionsSigned permutationsStandard tableauxto alternating sign matrixto increasing treebinary search tree: left to rightdescent wordconnectivity setdescent topsdescent bottomsleft-to-right-maxima to Dyck pathgraph of inversionsDEX compositiondescent compositioncycle typeLLPSRobinson-Schensted tableau shapelattice of intervalsparking functioncactus 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 notationpattern posetpermutation posetto cycle typeweak exceedance partitionto signed permutationRobinson-Schensted insertion tableauRobinson-Schensted recording tableau