There are 12 maps with codomain Standard tableaux 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
Dyck pathsInteger partitionsPermutationsSet partitionsStandard tableauxStandard tableauxto two-row standard tableauinitial tableaureading tableauRobinson-Schensted insertion tableauRobinson-Schensted recording tableauStandard tableau associated to a set partitioncatabolisminverse promotionpromotionrow-to-column-descentsconjugateSchützenberger involution