**Identifier**

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

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

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

transpose

Mp00006Alternating sign matrices ⟶ Alternating sign matrices

gyration

Mp00007Alternating sign matrices ⟶ Dyck paths

to Dyck path

Mp00098Alternating sign matrices ⟶ Perfect matchings

link pattern

**Binary trees**(14 maps) # tree like structures # Catalan objects # graph like objects

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**(6 maps) # word like objects # path like objects

Mp00096Binary words ⟶ Binary words

Foata bijection

Mp00097Binary words ⟶ Integer compositions

delta morphism

Mp00104Binary words ⟶ Binary words

reverse

Mp00105Binary words ⟶ Binary words

complement

Mp00135Binary words ⟶ Binary words

rotate front-to-back

Mp00136Binary words ⟶ Binary words

rotate back-to-front

**Cores**(2 maps) # partition like objects

**Dyck paths**(34 maps) # Catalan objects # path like objects

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

reverse

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

promotion

Mp00143Dyck paths ⟶ Dyck paths

inverse promotion

Mp00146Dyck 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

Mp00038Integer compositions ⟶ Integer compositions

reverse

Mp00039Integer compositions ⟶ Integer compositions

complement

Mp00040Integer compositions ⟶ Integer partitions

to partition

Mp00041Integer compositions ⟶ Integer compositions

conjugate

Mp00094Integer compositions ⟶ Binary words

to binary word

Mp00133Integer compositions ⟶ Integer compositions

delta morphism

**Integer partitions**(5 maps) # partition like objects

**Ordered trees**(7 maps) # tree like structures # Catalan objects # graph like objects

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) # word like objects # path like objects

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**(6 maps) # graph like objects

Mp00058Perfect matchings ⟶ Permutations

to permutation

Mp00092Perfect matchings ⟶ Set partitions

to set partition

Mp00113Perfect matchings ⟶ Perfect matchings

reverse

Mp00116Perfect matchings ⟶ Perfect matchings

Kasraoui-Zeng

Mp00144Perfect matchings ⟶ Perfect matchings

rotation

Mp00145Perfect matchings ⟶ Perfect matchings

inverse rotation

**Permutations**(27 maps) # word like objects

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

reverse

Mp00065Permutations ⟶ Posets

permutation poset

Mp00066Permutations ⟶ Permutations

inverse

Mp00067Permutations ⟶ Permutations

Foata bijection

Mp00068Permutations ⟶ Permutations

Simion-Schmidt map

Mp00069Permutations ⟶ Permutations

complement

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

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

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

**Set partitions**(6 maps) # partition like objects

Mp00079Set partitions ⟶ Integer partitions

shape

Mp00080Set partitions ⟶ Permutations

to permutation

Mp00091Set partitions ⟶ Set partitions

Cyclic rotation

Mp00112Set partitions ⟶ Set partitions

reverse

Mp00115Set partitions ⟶ Set partitions

Kasraoui-Zeng

Mp00128Set partitions ⟶ Integer compositions

to composition

**Standard tableaux**(7 maps) # tableau like objects

Mp00081Standard tableaux ⟶ Permutations

reading word permutation

Mp00082Standard tableaux ⟶ Gelfand-Tsetlin patterns

to Gelfand-Tsetlin pattern

Mp00083Standard tableaux ⟶ Integer partitions

shape

Mp00084Standard tableaux ⟶ Standard tableaux

conjugate

Mp00085Standard tableaux ⟶ Standard tableaux

Schützenberger involution

Mp00106Standard tableaux ⟶ Standard tableaux

catabolism

Mp00134Standard tableaux ⟶ Binary words

descent word