There are 45 maps with domain Dyck paths 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
Dyck pathsAlternating sign matricesBinary treesBinary wordsDyck pathsInteger compositionsInteger partitionsOrdered treesPerfect matchingsPermutationsPosetsSet partitionsSkew partitionsStandard tableauxto symmetric ASMto alternating sign matrixlogarithmic height to pruning numberto binary tree: left tree, up step, right tree, down stepto binary tree: up step, left tree, down step, right treeto binary worddecomposition reversepeeling mapswap returns and last descentLalanne-Kreweras involutionCori-Le Borgne involutionElizalde-Deutsch bijectionBarnabei-Castronuovo involutionAdin-Bagno-Roichman transformationswitch returns and last double risepromotioninverse promotionprime Dyck pathpeaks-to-valleysDelest-Viennot-inversereflect parallelogram polyominoDelest-ViennotreverseKnuth-Krattenthalerzeta mapinverse zeta mapinverse Kreweras complementbounce pathtouch compositionrise compositionto partitionto ordered treeto tunnel matchingto 321-avoiding permutation (Krattenthaler)to 321-avoiding permutation (Billey-Jockusch-Stanley)Ringelto non-crossing permutationto 321-avoiding permutationto 132-avoiding permutationto 312-avoiding permutationparallelogram posetHessenberg posetto noncrossing partitionskew partitionto two-row standard tableau