There are 14 maps with codomain Posets 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
Binary treesBinary wordsDyck pathsFinite Cartan typesGraphsLatticesOrdered treesPermutationsPosetsSemistandard tableauxSkew partitionsPosetsto posetposet of factorsparallelogram posetHessenberg posetto root posetweak duplicate orderto posetjoin irreduciblesto posetpattern posetpermutation posetdual posetsubcrystalcell poset