Identifier
All 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