Maps database

Identifier
      
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All 133 maps in the database:
   Alternating sign matrices (8 maps) # matrix like objects
to semistandard tableau
to left key permutation
rotate counterclockwise
rotate clockwise
transpose
gyration
to Dyck path
link pattern
   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
Foata bijection
delta morphism
reverse
complement
   Cores (2 maps) # partition like objects
to bounded partition
to partition
   Dyck paths (29 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)
switch returns and last double rise
   Gelfand-Tsetlin patterns (1 maps) # matrix like objects
to semistandard tableau
   Graphs (3 maps) # graph like objects
to partition of connected components
complement
Ore closure
   Integer compositions (6 maps) # partition like objects
reverse
complement
to partition
conjugate
to binary word
delta morphism
   Integer partitions (5 maps) # partition like objects
initial tableau
to Dyck path
conjugate
reading tableau
to binary word
   Ordered trees (6 maps) # tree like structures # Catalan objects # graph like objects
to graph
to poset
left-right symmetry
to binary tree: left brother = left child
to binary tree: right brother = right child
to Dyck path
   Parking functions (6 maps) # word like objects # path like objects
to non-decreasing parking function
to car permutation
to inverse des composition
to labelling permutation
to Dyck path
to touch composition
   Perfect matchings (4 maps) # graph like objects
to permutation
to set partition
reverse
Kasraoui-Zeng
   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
to graph
Greene-Kleitman invariant
dual poset
   Semistandard tableaux (5 maps) # tableau like objects
reading word permutation
to Gelfand-Tsetlin pattern
shape
Schuetzenberger involution
catabolism
   Set partitions (5 maps) # partition like objects
shape
to permutation
Cyclic rotation
reverse
Kasraoui-Zeng
   Standard tableaux (6 maps) # tableau like objects
reading word permutation
to Gelfand-Tsetlin pattern
shape
conjugate
Schuetzenberger involution
catabolism