Maps database

**All 131 maps**in the database:

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

**Binary trees**(13 maps) # tree like structures # Catalan objects # graph like objects

to complete tree

left rotate

to ordered tree: left child = left brother

to graph

to Dyck path: up step, left tree, down step, right tree

to poset

to 132-avoiding permutation

to ordered tree: right child = right brother

left-right symmetry

to 312-avoiding permutation

left border symmetry

right rotate

to Tamari-corresponding Dyck path

**Binary words**(4 maps) # word like objects # path like objects

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

**Dyck paths**(28 maps) # Catalan objects # path like objects

to non-crossing permutation

to 321-avoiding permutation

to 132-avoiding permutation

to ordered tree

to partition

reverse

to Tamari-corresponding binary tree

zeta map

to 312-avoiding permutation

inverse zeta map

to two-row standard tableau

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

to alternating sign matrix

to binary word

bounce path

touch composition

decomposition reverse

rise composition

peeling map

swap returns and last-descent

to 321-avoiding permutation (Krattenthaler)

Lalanne-Kreweras involution

Cori-Le Borgne involution

Elizalde-Deutsch bijection

Barnabei-Castronuovo involution

Adin-Bagno-Roichman transformation

Barnabei-Castronuovo involution

to 321-avoiding permutation (Billey-Jokusch-Stanley)

**Gelfand-Tsetlin patterns**(1 maps) # matrix like objects

to semistandard tableau

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

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

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

**Ordered trees**(6 maps) # tree like structures # Catalan objects # graph like objects

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

**Perfect matchings**(4 maps) # graph like objects

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

Robinson-Schensted insertion tableau

Robinson-Schensted tableau shape

to increasing tree

inversion-number to major-index bijection

to alternating sign matrix

reverse

permutation poset

inverse

Foata bijection

Simion-Schmidt map

complement

Robinson-Schensted recording tableau

descent composition

binary search tree: left to right

major-index to inversion-number bijection

first fundamental transformation

inverse first fundamental transformation

Kreweras complement

Inverse Kreweras complement

cycle-as-one-line notation

cycle type

descent word

connectivity set

cactus evacuation

left-to-right-maxima to Dyck path

descent tops

descent bottoms

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

**Semistandard tableaux**(5 maps) # tableau like objects

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

**Standard tableaux**(6 maps) # tableau like objects