Identifier
There are 146 maps in the database:
   Alternating sign matrices (8 maps) # matrix like objects
Mp00001 Alternating sign matrices ⟶ Semistandard tableaux
to semistandard tableau
Mp00002 Alternating sign matrices ⟶ Permutations
to left key permutation
Mp00003 Alternating sign matrices ⟶ Alternating sign matrices
rotate counterclockwise
Mp00004 Alternating sign matrices ⟶ Alternating sign matrices
rotate clockwise
Mp00005 Alternating sign matrices ⟶ Alternating sign matrices
transpose
Mp00006 Alternating sign matrices ⟶ Alternating sign matrices
gyration
Mp00007 Alternating sign matrices ⟶ Dyck paths
to Dyck path
Mp00098 Alternating sign matrices ⟶ Perfect matchings
link pattern
   Binary trees (14 maps) # tree like structures # Catalan objects # graph like objects
Mp00008 Binary trees ⟶ Ordered trees
to complete tree
Mp00009 Binary trees ⟶ Binary trees
left rotate
Mp00010 Binary trees ⟶ Ordered trees
to ordered tree: left child = left brother
Mp00011 Binary trees ⟶ Graphs
to graph
Mp00012 Binary trees ⟶ Dyck paths
to Dyck path: up step, left tree, down step, right tree
Mp00013 Binary trees ⟶ Posets
to poset
Mp00014 Binary trees ⟶ Permutations
to 132-avoiding permutation
Mp00015 Binary trees ⟶ Ordered trees
to ordered tree: right child = right brother
Mp00016 Binary trees ⟶ Binary trees
left-right symmetry
Mp00017 Binary trees ⟶ Permutations
to 312-avoiding permutation
Mp00018 Binary trees ⟶ Binary trees
left border symmetry
Mp00019 Binary trees ⟶ Binary trees
right rotate
Mp00020 Binary trees ⟶ Dyck paths
to Tamari-corresponding Dyck path
Mp00141 Binary trees ⟶ Dyck paths
pruning number to logarithmic height
   Binary words (6 maps) # word like objects # path like objects
Mp00096 Binary words ⟶ Binary words
Foata bijection
Mp00097 Binary words ⟶ Integer compositions
delta morphism
Mp00104 Binary words ⟶ Binary words
reverse
Mp00105 Binary words ⟶ Binary words
complement
Mp00135 Binary words ⟶ Binary words
rotate front-to-back
Mp00136 Binary words ⟶ Binary words
rotate back-to-front
   Cores (2 maps) # partition like objects
Mp00021 Cores ⟶ Integer partitions
to bounded partition
Mp00022 Cores ⟶ Integer partitions
to partition
   Dyck paths (34 maps) # Catalan objects # path like objects
Mp00023 Dyck paths ⟶ Permutations
to non-crossing permutation
Mp00024 Dyck paths ⟶ Permutations
to 321-avoiding permutation
Mp00025 Dyck paths ⟶ Permutations
to 132-avoiding permutation
Mp00026 Dyck paths ⟶ Ordered trees
to ordered tree
Mp00027 Dyck paths ⟶ Integer partitions
to partition
Mp00028 Dyck paths ⟶ Dyck paths
reverse
Mp00029 Dyck paths ⟶ Binary trees
to Tamari-corresponding binary tree
Mp00030 Dyck paths ⟶ Dyck paths
zeta map
Mp00031 Dyck paths ⟶ Permutations
to 312-avoiding permutation
Mp00032 Dyck paths ⟶ Dyck paths
inverse zeta map
Mp00033 Dyck paths ⟶ Standard tableaux
to two-row standard tableau
Mp00034 Dyck paths ⟶ Binary trees
to binary tree: up step, left tree, down step, right tree
Mp00035 Dyck paths ⟶ Alternating sign matrices
to alternating sign matrix
Mp00093 Dyck paths ⟶ Binary words
to binary word
Mp00099 Dyck paths ⟶ Dyck paths
bounce path
Mp00100 Dyck paths ⟶ Integer compositions
touch composition
Mp00101 Dyck paths ⟶ Dyck paths
decomposition reverse
Mp00102 Dyck paths ⟶ Integer compositions
rise composition
Mp00103 Dyck paths ⟶ Dyck paths
peeling map
Mp00118 Dyck paths ⟶ Dyck paths
swap returns and last-descent
Mp00119 Dyck paths ⟶ Permutations
to 321-avoiding permutation (Krattenthaler)
Mp00120 Dyck paths ⟶ Dyck paths
Lalanne-Kreweras involution
Mp00121 Dyck paths ⟶ Dyck paths
Cori-Le Borgne involution
Mp00122 Dyck paths ⟶ Dyck paths
Elizalde-Deutsch bijection
Mp00123 Dyck paths ⟶ Dyck paths
Barnabei-Castronuovo involution
Mp00124 Dyck paths ⟶ Dyck paths
Adin-Bagno-Roichman transformation
Mp00129 Dyck paths ⟶ Permutations
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Mp00132 Dyck paths ⟶ Dyck paths
switch returns and last double rise
Mp00137 Dyck paths ⟶ Alternating sign matrices
to symmetric ASM
Mp00138 Dyck paths ⟶ Set partitions
to noncrossing partition
Mp00140 Dyck paths ⟶ Binary trees
logarithmic height to pruning number
Mp00142 Dyck paths ⟶ Dyck paths
promotion
Mp00143 Dyck paths ⟶ Dyck paths
inverse promotion
Mp00146 Dyck paths ⟶ Perfect matchings
to noncrossing matching
   Gelfand-Tsetlin patterns (1 maps) # matrix like objects
Mp00036 Gelfand-Tsetlin patterns ⟶ Semistandard tableaux
to semistandard tableau
   Graphs (3 maps) # graph like objects
Mp00037 Graphs ⟶ Integer partitions
to partition of connected components
Mp00111 Graphs ⟶ Graphs
complement
Mp00117 Graphs ⟶ Graphs
Ore closure
   Integer compositions (6 maps) # partition like objects
Mp00038 Integer compositions ⟶ Integer compositions
reverse
Mp00039 Integer compositions ⟶ Integer compositions
complement
Mp00040 Integer compositions ⟶ Integer partitions
to partition
Mp00041 Integer compositions ⟶ Integer compositions
conjugate
Mp00094 Integer compositions ⟶ Binary words
to binary word
Mp00133 Integer compositions ⟶ Integer compositions
delta morphism
   Integer partitions (5 maps) # partition like objects
Mp00042 Integer partitions ⟶ Standard tableaux
initial tableau
Mp00043 Integer partitions ⟶ Dyck paths
to Dyck path
Mp00044 Integer partitions ⟶ Integer partitions
conjugate
Mp00045 Integer partitions ⟶ Standard tableaux
reading tableau
Mp00095 Integer partitions ⟶ Binary words
to binary word
   Ordered trees (7 maps) # tree like structures # Catalan objects # graph like objects
Mp00046 Ordered trees ⟶ Graphs
to graph
Mp00047 Ordered trees ⟶ Posets
to poset
Mp00048 Ordered trees ⟶ Ordered trees
left-right symmetry
Mp00049 Ordered trees ⟶ Binary trees
to binary tree: left brother = left child
Mp00050 Ordered trees ⟶ Binary trees
to binary tree: right brother = right child
Mp00051 Ordered trees ⟶ Dyck paths
to Dyck path
Mp00139 Ordered trees ⟶ Binary trees
Zeilberger's Strahler bijection
   Parking functions (6 maps) # word like objects # path like objects
Mp00052 Parking functions ⟶ Parking functions
to non-decreasing parking function
Mp00053 Parking functions ⟶ Permutations
to car permutation
Mp00054 Parking functions ⟶ Integer compositions
to inverse des composition
Mp00055 Parking functions ⟶ Permutations
to labelling permutation
Mp00056 Parking functions ⟶ Dyck paths
to Dyck path
Mp00057 Parking functions ⟶ Integer compositions
to touch composition
   Perfect matchings (6 maps) # graph like objects
Mp00058 Perfect matchings ⟶ Permutations
to permutation
Mp00092 Perfect matchings ⟶ Set partitions
to set partition
Mp00113 Perfect matchings ⟶ Perfect matchings
reverse
Mp00116 Perfect matchings ⟶ Perfect matchings
Kasraoui-Zeng
Mp00144 Perfect matchings ⟶ Perfect matchings
rotation
Mp00145 Perfect matchings ⟶ Perfect matchings
inverse rotation
   Permutations (27 maps) # word like objects
Mp00059 Permutations ⟶ Standard tableaux
Robinson-Schensted insertion tableau
Mp00060 Permutations ⟶ Integer partitions
Robinson-Schensted tableau shape
Mp00061 Permutations ⟶ Binary trees
to increasing tree
Mp00062 Permutations ⟶ Permutations
inversion-number to major-index bijection
Mp00063 Permutations ⟶ Alternating sign matrices
to alternating sign matrix
Mp00064 Permutations ⟶ Permutations
reverse
Mp00065 Permutations ⟶ Posets
permutation poset
Mp00066 Permutations ⟶ Permutations
inverse
Mp00067 Permutations ⟶ Permutations
Foata bijection
Mp00068 Permutations ⟶ Permutations
Simion-Schmidt map
Mp00069 Permutations ⟶ Permutations
complement
Mp00070 Permutations ⟶ Standard tableaux
Robinson-Schensted recording tableau
Mp00071 Permutations ⟶ Integer compositions
descent composition
Mp00072 Permutations ⟶ Binary trees
binary search tree: left to right
Mp00073 Permutations ⟶ Permutations
major-index to inversion-number bijection
Mp00086 Permutations ⟶ Permutations
first fundamental transformation
Mp00087 Permutations ⟶ Permutations
inverse first fundamental transformation
Mp00088 Permutations ⟶ Permutations
Kreweras complement
Mp00089 Permutations ⟶ Permutations
Inverse Kreweras complement
Mp00090 Permutations ⟶ Permutations
cycle-as-one-line notation
Mp00108 Permutations ⟶ Integer partitions
cycle type
Mp00109 Permutations ⟶ Binary words
descent word
Mp00114 Permutations ⟶ Binary words
connectivity set
Mp00126 Permutations ⟶ Permutations
cactus evacuation
Mp00127 Permutations ⟶ Dyck paths
left-to-right-maxima to Dyck path
Mp00130 Permutations ⟶ Binary words
descent tops
Mp00131 Permutations ⟶ Binary words
descent bottoms
   Posets (3 maps) # graph like objects
Mp00074 Posets ⟶ Graphs
to graph
Mp00110 Posets ⟶ Integer partitions
Greene-Kleitman invariant
Mp00125 Posets ⟶ Posets
dual poset
   Semistandard tableaux (5 maps) # tableau like objects
Mp00075 Semistandard tableaux ⟶ Permutations
reading word permutation
Mp00076 Semistandard tableaux ⟶ Gelfand-Tsetlin patterns
to Gelfand-Tsetlin pattern
Mp00077 Semistandard tableaux ⟶ Integer partitions
shape
Mp00078 Semistandard tableaux ⟶ Semistandard tableaux
Schuetzenberger involution
Mp00107 Semistandard tableaux ⟶ Semistandard tableaux
catabolism
   Set partitions (6 maps) # partition like objects
Mp00079 Set partitions ⟶ Integer partitions
shape
Mp00080 Set partitions ⟶ Permutations
to permutation
Mp00091 Set partitions ⟶ Set partitions
Cyclic rotation
Mp00112 Set partitions ⟶ Set partitions
reverse
Mp00115 Set partitions ⟶ Set partitions
Kasraoui-Zeng
Mp00128 Set partitions ⟶ Integer compositions
to composition
   Standard tableaux (7 maps) # tableau like objects
Mp00081 Standard tableaux ⟶ Permutations
reading word permutation
Mp00082 Standard tableaux ⟶ Gelfand-Tsetlin patterns
to Gelfand-Tsetlin pattern
Mp00083 Standard tableaux ⟶ Integer partitions
shape
Mp00084 Standard tableaux ⟶ Standard tableaux
conjugate
Mp00085 Standard tableaux ⟶ Standard tableaux
Schuetzenberger involution
Mp00106 Standard tableaux ⟶ Standard tableaux
catabolism
Mp00134 Standard tableaux ⟶ Binary words
descent word