There are 12 maps with codomain Binary 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 treesPermutationsBinary treesleft-right symmetryleft border symmetryright rotateleft rotatelogarithmic height to pruning numberto binary tree: left tree, up step, right tree, down stepto binary tree: up step, left tree, down step, right treeZeilberger's Strahler bijectionto binary tree: left brother = left childto binary tree: right brother = right childto increasing treebinary search tree: left to right