searching the database
Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St001440
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001440: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001440: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,2] => [1,1]
=> [1]
=> 0
[1,-2] => [1,2] => [1,1]
=> [1]
=> 0
[-1,2] => [1,2] => [1,1]
=> [1]
=> 0
[-1,-2] => [1,2] => [1,1]
=> [1]
=> 0
[1,2,3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 1
[1,2,-3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 1
[1,-2,3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 1
[1,-2,-3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 1
[-1,2,3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 1
[-1,2,-3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 1
[-1,-2,3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 1
[-1,-2,-3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 1
[1,3,2] => [1,3,2] => [2,1]
=> [1]
=> 0
[1,3,-2] => [1,3,2] => [2,1]
=> [1]
=> 0
[1,-3,2] => [1,3,2] => [2,1]
=> [1]
=> 0
[1,-3,-2] => [1,3,2] => [2,1]
=> [1]
=> 0
[-1,3,2] => [1,3,2] => [2,1]
=> [1]
=> 0
[-1,3,-2] => [1,3,2] => [2,1]
=> [1]
=> 0
[-1,-3,2] => [1,3,2] => [2,1]
=> [1]
=> 0
[-1,-3,-2] => [1,3,2] => [2,1]
=> [1]
=> 0
[2,1,3] => [2,1,3] => [2,1]
=> [1]
=> 0
[2,1,-3] => [2,1,3] => [2,1]
=> [1]
=> 0
[2,-1,3] => [2,1,3] => [2,1]
=> [1]
=> 0
[2,-1,-3] => [2,1,3] => [2,1]
=> [1]
=> 0
[-2,1,3] => [2,1,3] => [2,1]
=> [1]
=> 0
[-2,1,-3] => [2,1,3] => [2,1]
=> [1]
=> 0
[-2,-1,3] => [2,1,3] => [2,1]
=> [1]
=> 0
[-2,-1,-3] => [2,1,3] => [2,1]
=> [1]
=> 0
[3,2,1] => [3,2,1] => [2,1]
=> [1]
=> 0
[3,2,-1] => [3,2,1] => [2,1]
=> [1]
=> 0
[3,-2,1] => [3,2,1] => [2,1]
=> [1]
=> 0
[3,-2,-1] => [3,2,1] => [2,1]
=> [1]
=> 0
[-3,2,1] => [3,2,1] => [2,1]
=> [1]
=> 0
[-3,2,-1] => [3,2,1] => [2,1]
=> [1]
=> 0
[-3,-2,1] => [3,2,1] => [2,1]
=> [1]
=> 0
[-3,-2,-1] => [3,2,1] => [2,1]
=> [1]
=> 0
[1,2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,2,3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,2,-3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,2,-3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,-3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,2,3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,2,-3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,2,-3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,-2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,-2,3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 0
Description
The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition.
Matching statistic: St001857
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001857: Signed permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 67%
Mp00069: Permutations —complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001857: Signed permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 67%
Values
[1,2] => [1,2] => [2,1] => [2,1] => 0
[1,-2] => [1,2] => [2,1] => [2,1] => 0
[-1,2] => [1,2] => [2,1] => [2,1] => 0
[-1,-2] => [1,2] => [2,1] => [2,1] => 0
[1,2,3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[1,2,-3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[1,-2,3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[1,-2,-3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[-1,2,3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[-1,2,-3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[-1,-2,3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[-1,-2,-3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[1,3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[1,3,-2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[1,-3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[1,-3,-2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[-1,3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[-1,3,-2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[-1,-3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[-1,-3,-2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[2,1,3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[2,1,-3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[2,-1,3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[2,-1,-3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[-2,1,3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[-2,1,-3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[-2,-1,3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[-2,-1,-3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[3,2,1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[3,2,-1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[3,-2,1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[3,-2,-1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[-3,2,1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[-3,2,-1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[-3,-2,1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[-3,-2,-1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[1,2,3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[1,2,3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[1,2,-3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[1,2,-3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[1,-2,3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[1,-2,3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[1,-2,-3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[1,-2,-3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[-1,2,3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[-1,2,3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[-1,2,-3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[-1,2,-3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[-1,-2,3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[-1,-2,3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[-1,-2,-3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[-1,-2,-3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[1,2,4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,2,4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,2,-4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,2,-4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,-2,4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,-2,4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,-2,-4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,-2,-4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,2,4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,2,4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,2,-4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,2,-4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,-2,4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,-2,4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,-2,-4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,-2,-4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,3,2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,3,2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,3,-2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,3,-2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,-3,2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,-3,2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,-3,-2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,-3,-2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,3,2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,3,2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,3,-2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,3,-2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,-3,2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,-3,2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,-3,-2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,-3,-2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,3,4,2] => [1,3,4,2] => [4,2,1,3] => [4,2,1,3] => ? = 0
[1,3,4,-2] => [1,3,4,2] => [4,2,1,3] => [4,2,1,3] => ? = 0
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.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!