There are 233 maps in the database. There are possibly some more waiting for verification.

Mp00001Alternating sign matrices ⟶ Semistandard tableaux
to semistandard tableau via monotone triangles
Mp00002Alternating sign matrices ⟶ Permutations
to left key permutation
Mp00003Alternating sign matrices ⟶ Alternating sign matrices
rotate counterclockwise
Mp00004Alternating sign matrices ⟶ Alternating sign matrices
rotate clockwise
Mp00005Alternating sign matrices ⟶ Alternating sign matrices
Mp00006Alternating sign matrices ⟶ Alternating sign matrices
Mp00007Alternating sign matrices ⟶ Dyck paths
to Dyck path
Mp00098Alternating sign matrices ⟶ Perfect matchings
link pattern
   Binary trees (14 maps)
Mp00008Binary trees ⟶ Ordered trees
to complete tree
Mp00009Binary trees ⟶ Binary trees
left rotate
Mp00010Binary trees ⟶ Ordered trees
to ordered tree: left child = left brother
Mp00011Binary trees ⟶ Graphs
to graph
Mp00012Binary trees ⟶ Dyck paths
to Dyck path: up step, left tree, down step, right tree
Mp00013Binary trees ⟶ Posets
to poset
Mp00014Binary trees ⟶ Permutations
to 132-avoiding permutation
Mp00015Binary trees ⟶ Ordered trees
to ordered tree: right child = right brother
Mp00016Binary trees ⟶ Binary trees
left-right symmetry
Mp00017Binary trees ⟶ Permutations
to 312-avoiding permutation
Mp00018Binary trees ⟶ Binary trees
left border symmetry
Mp00019Binary trees ⟶ Binary trees
right rotate
Mp00020Binary trees ⟶ Dyck paths
to Tamari-corresponding Dyck path
Mp00141Binary trees ⟶ Dyck paths
pruning number to logarithmic height
   Binary words (10 maps)
Mp00096Binary words ⟶ Binary words
Foata bijection
Mp00097Binary words ⟶ Integer compositions
delta morphism
Mp00104Binary words ⟶ Binary words
Mp00105Binary words ⟶ Binary words
Mp00135Binary words ⟶ Binary words
rotate front-to-back
Mp00136Binary words ⟶ Binary words
rotate back-to-front
Mp00158Binary words ⟶ Binary words
alternating inverse
Mp00178Binary words ⟶ Integer compositions
to composition
Mp00200Binary words ⟶ Binary words
Mp00224Binary words ⟶ Binary words
   Cores (2 maps)
Mp00021Cores ⟶ Integer partitions
to bounded partition
Mp00022Cores ⟶ Integer partitions
to partition
   Dyck paths (42 maps)
Mp00023Dyck paths ⟶ Permutations
to non-crossing permutation
Mp00024Dyck paths ⟶ Permutations
to 321-avoiding permutation
Mp00025Dyck paths ⟶ Permutations
to 132-avoiding permutation
Mp00026Dyck paths ⟶ Ordered trees
to ordered tree
Mp00027Dyck paths ⟶ Integer partitions
to partition
Mp00028Dyck paths ⟶ Dyck paths
Mp00029Dyck paths ⟶ Binary trees
to binary tree: left tree, up step, right tree, down step
Mp00030Dyck paths ⟶ Dyck paths
zeta map
Mp00031Dyck paths ⟶ Permutations
to 312-avoiding permutation
Mp00032Dyck paths ⟶ Dyck paths
inverse zeta map
Mp00033Dyck paths ⟶ Standard tableaux
to two-row standard tableau
Mp00034Dyck paths ⟶ Binary trees
to binary tree: up step, left tree, down step, right tree
Mp00035Dyck paths ⟶ Alternating sign matrices
to alternating sign matrix
Mp00093Dyck paths ⟶ Binary words
to binary word
Mp00099Dyck paths ⟶ Dyck paths
bounce path
Mp00100Dyck paths ⟶ Integer compositions
touch composition
Mp00101Dyck paths ⟶ Dyck paths
decomposition reverse
Mp00102Dyck paths ⟶ Integer compositions
rise composition
Mp00103Dyck paths ⟶ Dyck paths
peeling map
Mp00118Dyck paths ⟶ Dyck paths
swap returns and last descent
Mp00119Dyck paths ⟶ Permutations
to 321-avoiding permutation (Krattenthaler)
Mp00120Dyck paths ⟶ Dyck paths
Lalanne-Kreweras involution
Mp00121Dyck paths ⟶ Dyck paths
Cori-Le Borgne involution
Mp00122Dyck paths ⟶ Dyck paths
Elizalde-Deutsch bijection
Mp00123Dyck paths ⟶ Dyck paths
Barnabei-Castronuovo involution
Mp00124Dyck paths ⟶ Dyck paths
Adin-Bagno-Roichman transformation
Mp00129Dyck paths ⟶ Permutations
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Mp00132Dyck paths ⟶ Dyck paths
switch returns and last double rise
Mp00137Dyck paths ⟶ Alternating sign matrices
to symmetric ASM
Mp00138Dyck paths ⟶ Set partitions
to noncrossing partition
Mp00140Dyck paths ⟶ Binary trees
logarithmic height to pruning number
Mp00142Dyck paths ⟶ Dyck paths
Mp00143Dyck paths ⟶ Dyck paths
inverse promotion
Mp00146Dyck paths ⟶ Perfect matchings
to tunnel matching
Mp00199Dyck paths ⟶ Dyck paths
prime Dyck path
Mp00201Dyck paths ⟶ Permutations
Mp00222Dyck paths ⟶ Dyck paths
Mp00227Dyck paths ⟶ Dyck paths
Mp00228Dyck paths ⟶ Dyck paths
reflect parallelogram polyomino
Mp00229Dyck paths ⟶ Dyck paths
Mp00232Dyck paths ⟶ Posets
parallelogram poset
Mp00233Dyck paths ⟶ Skew partitions
skew partition
   Finite Cartan types (1 maps)
Mp00148Finite Cartan types ⟶ Posets
to root poset
   Gelfand-Tsetlin patterns (6 maps)
Mp00036Gelfand-Tsetlin patterns ⟶ Semistandard tableaux
to semistandard tableau
Mp00078Gelfand-Tsetlin patterns ⟶ Gelfand-Tsetlin patterns
Schuetzenberger involution
Mp00210Gelfand-Tsetlin patterns ⟶ Gelfand-Tsetlin patterns
Mp00211Gelfand-Tsetlin patterns ⟶ Gelfand-Tsetlin patterns
inverse promotion
Mp00212Gelfand-Tsetlin patterns ⟶ Gelfand-Tsetlin patterns
inverse cycle
Mp00213Gelfand-Tsetlin patterns ⟶ Gelfand-Tsetlin patterns
   Graphs (9 maps)
Mp00037Graphs ⟶ Integer partitions
to partition of connected components
Mp00111Graphs ⟶ Graphs
Mp00117Graphs ⟶ Graphs
Ore closure
Mp00147Graphs ⟶ Graphs
Mp00152Graphs ⟶ Integer compositions
Laplacian multiplicities
Mp00154Graphs ⟶ Graphs
Mp00156Graphs ⟶ Graphs
line graph
Mp00157Graphs ⟶ Graphs
connected complement
Mp00203Graphs ⟶ Graphs
   Integer compositions (11 maps)
Mp00038Integer compositions ⟶ Integer compositions
Mp00039Integer compositions ⟶ Integer compositions
Mp00040Integer compositions ⟶ Integer partitions
to partition
Mp00041Integer compositions ⟶ Integer compositions
Mp00094Integer compositions ⟶ Binary words
to binary word
Mp00133Integer compositions ⟶ Integer compositions
delta morphism
Mp00172Integer compositions ⟶ Integer compositions
rotate back to front
Mp00173Integer compositions ⟶ Integer compositions
rotate front to back
Mp00180Integer compositions ⟶ Skew partitions
to ribbon
Mp00184Integer compositions ⟶ Graphs
to threshold graph
Mp00231Integer compositions ⟶ Dyck paths
bounce path
   Integer partitions (8 maps)
Mp00042Integer partitions ⟶ Standard tableaux
initial tableau
Mp00043Integer partitions ⟶ Dyck paths
to Dyck path
Mp00044Integer partitions ⟶ Integer partitions
Mp00045Integer partitions ⟶ Standard tableaux
reading tableau
Mp00095Integer partitions ⟶ Binary words
to binary word
Mp00179Integer partitions ⟶ Skew partitions
to skew partition
Mp00202Integer partitions ⟶ Integer partitions
first row removal
Mp00230Integer partitions ⟶ Dyck paths
parallelogram polyomino
   Lattices (4 maps)
Mp00191Lattices ⟶ Lattices
Mp00193Lattices ⟶ Posets
to poset
Mp00196Lattices ⟶ Lattices
The modular quotient of a lattice.
Mp00197Lattices ⟶ Lattices
The lattice of congruences of a lattice.
   Ordered trees (7 maps)
Mp00046Ordered trees ⟶ Graphs
to graph
Mp00047Ordered trees ⟶ Posets
to poset
Mp00048Ordered trees ⟶ Ordered trees
left-right symmetry
Mp00049Ordered trees ⟶ Binary trees
to binary tree: left brother = left child
Mp00050Ordered trees ⟶ Binary trees
to binary tree: right brother = right child
Mp00051Ordered trees ⟶ Dyck paths
to Dyck path
Mp00139Ordered trees ⟶ Binary trees
Zeilberger's Strahler bijection
   Parking functions (6 maps)
Mp00052Parking functions ⟶ Parking functions
to non-decreasing parking function
Mp00053Parking functions ⟶ Permutations
to car permutation
Mp00054Parking functions ⟶ Integer compositions
to inverse des composition
Mp00055Parking functions ⟶ Permutations
to labelling permutation
Mp00056Parking functions ⟶ Dyck paths
to Dyck path
Mp00057Parking functions ⟶ Integer compositions
to touch composition
   Perfect matchings (8 maps)
Mp00058Perfect matchings ⟶ Permutations
to permutation
Mp00092Perfect matchings ⟶ Set partitions
to set partition
Mp00113Perfect matchings ⟶ Perfect matchings
Mp00116Perfect matchings ⟶ Perfect matchings
Mp00144Perfect matchings ⟶ Perfect matchings
Mp00145Perfect matchings ⟶ Perfect matchings
inverse rotation
Mp00150Perfect matchings ⟶ Dyck paths
to Dyck path
Mp00165Perfect matchings ⟶ Perfect matchings
Chen Deng Du Stanley Yan
   Permutations (37 maps)
Mp00059Permutations ⟶ Standard tableaux
Robinson-Schensted insertion tableau
Mp00060Permutations ⟶ Integer partitions
Robinson-Schensted tableau shape
Mp00061Permutations ⟶ Binary trees
to increasing tree
Mp00062Permutations ⟶ Permutations
Lehmer-code to major-code bijection
Mp00063Permutations ⟶ Alternating sign matrices
to alternating sign matrix
Mp00064Permutations ⟶ Permutations
Mp00065Permutations ⟶ Posets
permutation poset
Mp00066Permutations ⟶ Permutations
Mp00067Permutations ⟶ Permutations
Foata bijection
Mp00068Permutations ⟶ Permutations
Simion-Schmidt map
Mp00069Permutations ⟶ Permutations
Mp00070Permutations ⟶ Standard tableaux
Robinson-Schensted recording tableau
Mp00071Permutations ⟶ Integer compositions
descent composition
Mp00072Permutations ⟶ Binary trees
binary search tree: left to right
Mp00073Permutations ⟶ Permutations
major-index to inversion-number bijection
Mp00086Permutations ⟶ Permutations
first fundamental transformation
Mp00087Permutations ⟶ Permutations
inverse first fundamental transformation
Mp00088Permutations ⟶ Permutations
Kreweras complement
Mp00089Permutations ⟶ Permutations
Inverse Kreweras complement
Mp00090Permutations ⟶ Permutations
cycle-as-one-line notation
Mp00108Permutations ⟶ Integer partitions
cycle type
Mp00109Permutations ⟶ Binary words
descent word
Mp00114Permutations ⟶ Binary words
connectivity set
Mp00126Permutations ⟶ Permutations
cactus evacuation
Mp00127Permutations ⟶ Dyck paths
left-to-right-maxima to Dyck path
Mp00130Permutations ⟶ Binary words
descent tops
Mp00131Permutations ⟶ Binary words
descent bottoms
Mp00149Permutations ⟶ Permutations
Lehmer code rotation
Mp00151Permutations ⟶ Set partitions
to cycle type
Mp00159Permutations ⟶ Permutations
Demazure product with inverse
Mp00160Permutations ⟶ Graphs
graph of inversions
Mp00170Permutations ⟶ Signed permutations
to signed permutation
Mp00175Permutations ⟶ Permutations
inverse Foata bijection
Mp00204Permutations ⟶ Integer partitions
Mp00208Permutations ⟶ Lattices
lattice of intervals
Mp00209Permutations ⟶ Posets
pattern poset
Mp00223Permutations ⟶ Permutations
   Plane partitions (1 maps)
Mp00177Plane partitions ⟶ Plane partitions
   Posets (7 maps)
Mp00074Posets ⟶ Graphs
to graph
Mp00110Posets ⟶ Integer partitions
Greene-Kleitman invariant
Mp00125Posets ⟶ Posets
dual poset
Mp00195Posets ⟶ Lattices
order ideals
Mp00198Posets ⟶ Graphs
The incomparability graph of a poset.
Mp00205Posets ⟶ Lattices
maximal antichains
Mp00206Posets ⟶ Lattices
antichains of maximal size
   Semistandard tableaux (6 maps)
Mp00075Semistandard tableaux ⟶ Permutations
reading word permutation
Mp00076Semistandard tableaux ⟶ Gelfand-Tsetlin patterns
to Gelfand-Tsetlin pattern
Mp00077Semistandard tableaux ⟶ Integer partitions
Mp00107Semistandard tableaux ⟶ Semistandard tableaux
Mp00214Semistandard tableaux ⟶ Posets
Mp00225Semistandard tableaux ⟶ Integer partitions
   Set partitions (17 maps)
Mp00079Set partitions ⟶ Integer partitions
Mp00080Set partitions ⟶ Permutations
to permutation
Mp00091Set partitions ⟶ Set partitions
rotate increasing
Mp00112Set partitions ⟶ Set partitions
Mp00115Set partitions ⟶ Set partitions
Mp00128Set partitions ⟶ Integer compositions
to composition
Mp00164Set partitions ⟶ Set partitions
Chen Deng Du Stanley Yan
Mp00171Set partitions ⟶ Set partitions
intertwining number to dual major index
Mp00174Set partitions ⟶ Set partitions
dual major index to intertwining number
Mp00176Set partitions ⟶ Set partitions
rotate decreasing
Mp00215Set partitions ⟶ Set partitions
Mp00216Set partitions ⟶ Set partitions
inverse Wachs-White
Mp00217Set partitions ⟶ Set partitions
Mp00218Set partitions ⟶ Set partitions
inverse Wachs-White-rho
Mp00219Set partitions ⟶ Set partitions
inverse Yip
Mp00220Set partitions ⟶ Set partitions
Mp00221Set partitions ⟶ Set partitions
   Signed permutations (10 maps)
Mp00161Signed permutations ⟶ Signed permutations
Mp00162Signed permutations ⟶ Signed permutations
Mp00163Signed permutations ⟶ Permutations
Mp00166Signed permutations ⟶ Integer partitions
even cycle type
Mp00167Signed permutations ⟶ Signed permutations
inverse Kreweras complement
Mp00168Signed permutations ⟶ Signed permutations
Kreweras complement
Mp00169Signed permutations ⟶ Integer partitions
odd cycle type
Mp00188Signed permutations ⟶ Signed permutations
Mp00190Signed permutations ⟶ Signed permutations
Mp00194Signed permutations ⟶ Signed permutations
Foata-Han inverse
   Skew partitions (8 maps)
Mp00181Skew partitions ⟶ Integer compositions
row lengths
Mp00182Skew partitions ⟶ Integer partitions
outer shape
Mp00183Skew partitions ⟶ Integer partitions
inner shape
Mp00185Skew partitions ⟶ Posets
cell poset
Mp00186Skew partitions ⟶ Integer partitions
dominating partition
Mp00187Skew partitions ⟶ Skew partitions
Mp00189Skew partitions ⟶ Skew partitions
Mp00192Skew partitions ⟶ Lattices
dominating sublattice
   Standard tableaux (11 maps)
Mp00081Standard tableaux ⟶ Permutations
reading word permutation
Mp00082Standard tableaux ⟶ Gelfand-Tsetlin patterns
to Gelfand-Tsetlin pattern
Mp00083Standard tableaux ⟶ Integer partitions
Mp00084Standard tableaux ⟶ Standard tableaux
Mp00085Standard tableaux ⟶ Standard tableaux
Sch├╝tzenberger involution
Mp00106Standard tableaux ⟶ Standard tableaux
Mp00134Standard tableaux ⟶ Binary words
descent word
Mp00153Standard tableaux ⟶ Standard tableaux
inverse promotion
Mp00155Standard tableaux ⟶ Standard tableaux
Mp00207Standard tableaux ⟶ Integer compositions
horizontal strip sizes
Mp00226Standard tableaux ⟶ Standard tableaux