**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

**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

**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

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

**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