There are 14 maps with domain 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 treesBinary treesDyck pathsGraphsOrdered treesPermutationsPosetsleft-right symmetryleft border symmetryright rotateleft rotateto Dyck path: up step, left tree, down step, right treepruning number to logarithmic heightto Tamari-corresponding Dyck pathto graphto ordered tree: left child = left brotherto ordered tree: right child = right brotherto complete treeto 132-avoiding permutationto 312-avoiding permutationto poset