**Identifier**

**Alternating sign matrices**(8 maps) # matrix like objects

Mp00001
Alternating sign matrices ⟶ Semistandard tableaux

to semistandard tableau via monotone triangles

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

**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 binary tree: left tree, up step, right tree, down step

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 tunnel matching

**Gelfand-Tsetlin patterns**(2 maps) # matrix like objects

**Graphs**(3 maps) # graph like objects

**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

**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

Lehmer-code to major-code 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

**Semistandard tableaux**(4 maps) # tableau like objects

**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