There are 8 maps with codomain Ordered trees 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 treesDyck pathsOrdered treesParking functionsOrdered treesto ordered tree: left child = left brotherto ordered tree: right child = right brotherto complete treeto ordered treerotateDeBruijn-Morselt plane tree automorphismleft-right symmetryordered tree