There are 25 maps with codomain Integer compositions 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 pathsGraphsInteger compositionsOrdered set partitionsParking functionsPermutationsSet partitionsSkew partitionsStandard tableauxInteger compositionsto compositiondelta morphismtouch compositionrise compositionLaplacian multiplicitieschromatic difference sequencedelta morphismrotate back to frontrotate front to backFoata bijectioninverse Foata bijectionreversecomplementconjugateto compositionto compositionto inverse des compositionto touch compositionDEX compositiondescent compositionto compositionrow lengthshorizontal strip sizespeak compositionvalley composition