There are 27 maps with codomain Binary words 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 wordsDyck pathsInteger compositionsInteger partitionsPermutationsSigned permutationsStandard tableauxBinary wordsreversecomplementrotate front-to-backrotate back-to-frontalternating inversetwistrunsortvalleys-to-peaksBurrows-Wheelerzeros to flag zerosflag zeros to zerosGray nextGray previousrowmotionpath rowmotioninverse Foata bijectionFoata bijectionto binary wordto binary wordodd partsto binary worddescent wordconnectivity setdescent topsdescent bottomssignsdescent word