There are 32 maps with codomain Integer partitions 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
CoresDyck pathsGraphsInteger compositionsInteger partitionsPermutationsPlane partitionsPosetsSemistandard tableauxSet partitionsSigned permutationsSkew partitionsStandard tableauxInteger partitionsto bounded partitionto partitionto partitionclique sizesto edge-partition of connected componentsto edge-partition of biconnected componentsto partition of connected componentsto partitionfirst row removalBulgarian solitaireGlaisher-FranklinGlaisher-Franklin inverse2-conjugateLoehr-WarringtonLoehr-Warrington inverseconjugatecycle typeLLPSRobinson-Schensted tableau shapeto partitionGreene-Kleitman invariantrowmotion cycle typepromotion cycle typeweightshapeshapeeven cycle typeodd cycle typeouter shapeinner shapedominating partitionshape