Identifier
-
Mp00230:
Integer partitions
—parallelogram polyomino⟶
Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001857: Signed permutations ⟶ ℤ
Values
[1] => [1,0] => [1] => [1] => 0
[2] => [1,0,1,0] => [2,1] => [2,1] => 0
[1,1] => [1,1,0,0] => [1,2] => [1,2] => 0
[3] => [1,0,1,0,1,0] => [3,2,1] => [3,2,1] => 1
[2,1] => [1,0,1,1,0,0] => [2,3,1] => [2,3,1] => 0
[1,1,1] => [1,1,0,1,0,0] => [2,1,3] => [2,1,3] => 0
[2,2] => [1,1,1,0,0,0] => [1,2,3] => [1,2,3] => 0
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Description
The number of edges in the reduced word graph of a signed permutation.
The reduced word graph of a signed permutation π has the reduced words of π as vertices and an edge between two reduced words if they differ by exactly one braid move.
The reduced word graph of a signed permutation π has the reduced words of π as vertices and an edge between two reduced words if they differ by exactly one braid move.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
to signed permutation
Description
The signed permutation with all signs positive.
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