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: St000668
Mp00260: Signed permutations —Demazure product with inverse⟶ Signed permutations
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000668: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000668: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,2] => [1,1]
=> [2]
=> 2
[2,1] => [2,1] => [2]
=> [1,1]
=> 1
[-2,1] => [-2,-1] => [2]
=> [1,1]
=> 1
[1,2,3] => [1,2,3] => [1,1,1]
=> [3]
=> 3
[1,2,-3] => [1,2,-3] => [1,1]
=> [2]
=> 2
[1,3,2] => [1,3,2] => [2,1]
=> [2,1]
=> 2
[1,3,-2] => [1,-2,3] => [1,1]
=> [2]
=> 2
[1,-3,2] => [1,-3,-2] => [2,1]
=> [2,1]
=> 2
[2,1,3] => [2,1,3] => [2,1]
=> [2,1]
=> 2
[2,1,-3] => [2,1,-3] => [2]
=> [1,1]
=> 1
[-2,1,3] => [-2,-1,3] => [2,1]
=> [2,1]
=> 2
[-2,1,-3] => [-2,-1,-3] => [2]
=> [1,1]
=> 1
[2,3,1] => [3,2,1] => [2,1]
=> [2,1]
=> 2
[2,3,-1] => [-1,2,3] => [1,1]
=> [2]
=> 2
[2,-3,1] => [-3,2,-1] => [2,1]
=> [2,1]
=> 2
[-2,3,1] => [-2,-1,3] => [2,1]
=> [2,1]
=> 2
[-2,-3,1] => [-2,-1,-3] => [2]
=> [1,1]
=> 1
[3,1,2] => [3,2,1] => [2,1]
=> [2,1]
=> 2
[3,1,-2] => [3,-2,1] => [2]
=> [1,1]
=> 1
[-3,1,2] => [-3,2,-1] => [2,1]
=> [2,1]
=> 2
[-3,1,-2] => [-3,-2,-1] => [2]
=> [1,1]
=> 1
[3,2,1] => [3,2,1] => [2,1]
=> [2,1]
=> 2
[3,2,-1] => [-1,3,2] => [2]
=> [1,1]
=> 1
[3,-2,1] => [-2,-1,3] => [2,1]
=> [2,1]
=> 2
[-3,2,1] => [-3,2,-1] => [2,1]
=> [2,1]
=> 2
[-3,2,-1] => [-1,-3,-2] => [2]
=> [1,1]
=> 1
[-3,-2,1] => [-2,-1,-3] => [2]
=> [1,1]
=> 1
[1,2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [4]
=> 4
[1,2,3,-4] => [1,2,3,-4] => [1,1,1]
=> [3]
=> 3
[1,2,-3,4] => [1,2,-3,-4] => [1,1]
=> [2]
=> 2
[1,2,-3,-4] => [1,2,-3,-4] => [1,1]
=> [2]
=> 2
[1,-2,3,4] => [1,-2,-3,4] => [1,1]
=> [2]
=> 2
[-1,2,3,4] => [-1,-2,3,4] => [1,1]
=> [2]
=> 2
[1,2,4,3] => [1,2,4,3] => [2,1,1]
=> [3,1]
=> 3
[1,2,4,-3] => [1,2,-3,4] => [1,1,1]
=> [3]
=> 3
[1,2,-4,3] => [1,2,-4,-3] => [2,1,1]
=> [3,1]
=> 3
[1,2,-4,-3] => [1,2,-3,-4] => [1,1]
=> [2]
=> 2
[1,-2,4,3] => [1,-2,-3,4] => [1,1]
=> [2]
=> 2
[-1,2,4,3] => [-1,-2,4,3] => [2]
=> [1,1]
=> 1
[-1,2,-4,3] => [-1,-2,-4,-3] => [2]
=> [1,1]
=> 1
[1,3,2,4] => [1,3,2,4] => [2,1,1]
=> [3,1]
=> 3
[1,3,2,-4] => [1,3,2,-4] => [2,1]
=> [2,1]
=> 2
[1,3,-2,4] => [1,-2,3,-4] => [1,1]
=> [2]
=> 2
[1,3,-2,-4] => [1,-2,3,-4] => [1,1]
=> [2]
=> 2
[1,-3,2,4] => [1,-3,-2,4] => [2,1,1]
=> [3,1]
=> 3
[1,-3,2,-4] => [1,-3,-2,-4] => [2,1]
=> [2,1]
=> 2
[-1,3,2,4] => [-1,-2,3,4] => [1,1]
=> [2]
=> 2
[1,3,4,2] => [1,4,3,2] => [2,1,1]
=> [3,1]
=> 3
[1,3,4,-2] => [1,-2,3,4] => [1,1,1]
=> [3]
=> 3
[1,3,-4,2] => [1,-4,3,-2] => [2,1,1]
=> [3,1]
=> 3
Description
The least common multiple of the parts of the partition.
Matching statistic: St001232
Mp00260: Signed permutations —Demazure product with inverse⟶ Signed permutations
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 43% ●values known / values provided: 43%●distinct values known / distinct values provided: 83%
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 43% ●values known / values provided: 43%●distinct values known / distinct values provided: 83%
Values
[1,2] => [1,2] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[2,1] => [2,1] => [2]
=> [1,1,0,0,1,0]
=> 1
[-2,1] => [-2,-1] => [2]
=> [1,1,0,0,1,0]
=> 1
[1,2,3] => [1,2,3] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 3
[1,2,-3] => [1,2,-3] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,3,2] => [1,3,2] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[1,3,-2] => [1,-2,3] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,-3,2] => [1,-3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[2,1,3] => [2,1,3] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[2,1,-3] => [2,1,-3] => [2]
=> [1,1,0,0,1,0]
=> 1
[-2,1,3] => [-2,-1,3] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[-2,1,-3] => [-2,-1,-3] => [2]
=> [1,1,0,0,1,0]
=> 1
[2,3,1] => [3,2,1] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[2,3,-1] => [-1,2,3] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[2,-3,1] => [-3,2,-1] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[-2,3,1] => [-2,-1,3] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[-2,-3,1] => [-2,-1,-3] => [2]
=> [1,1,0,0,1,0]
=> 1
[3,1,2] => [3,2,1] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[3,1,-2] => [3,-2,1] => [2]
=> [1,1,0,0,1,0]
=> 1
[-3,1,2] => [-3,2,-1] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[-3,1,-2] => [-3,-2,-1] => [2]
=> [1,1,0,0,1,0]
=> 1
[3,2,1] => [3,2,1] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[3,2,-1] => [-1,3,2] => [2]
=> [1,1,0,0,1,0]
=> 1
[3,-2,1] => [-2,-1,3] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[-3,2,1] => [-3,2,-1] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[-3,2,-1] => [-1,-3,-2] => [2]
=> [1,1,0,0,1,0]
=> 1
[-3,-2,1] => [-2,-1,-3] => [2]
=> [1,1,0,0,1,0]
=> 1
[1,2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> 4
[1,2,3,-4] => [1,2,3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 3
[1,2,-3,4] => [1,2,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,2,-3,-4] => [1,2,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,-2,3,4] => [1,-2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[-1,2,3,4] => [-1,-2,3,4] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,2,4,3] => [1,2,4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[1,2,4,-3] => [1,2,-3,4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 3
[1,2,-4,3] => [1,2,-4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[1,2,-4,-3] => [1,2,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,-2,4,3] => [1,-2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[-1,2,4,3] => [-1,-2,4,3] => [2]
=> [1,1,0,0,1,0]
=> 1
[-1,2,-4,3] => [-1,-2,-4,-3] => [2]
=> [1,1,0,0,1,0]
=> 1
[1,3,2,4] => [1,3,2,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[1,3,2,-4] => [1,3,2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[1,3,-2,4] => [1,-2,3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,3,-2,-4] => [1,-2,3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,-3,2,4] => [1,-3,-2,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[1,-3,2,-4] => [1,-3,-2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[-1,3,2,4] => [-1,-2,3,4] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,3,4,2] => [1,4,3,2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[1,3,4,-2] => [1,-2,3,4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 3
[1,3,-4,2] => [1,-4,3,-2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[1,3,-4,-2] => [1,-2,3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,-3,4,2] => [1,-3,-2,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[1,-3,-4,2] => [1,-3,-2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[-1,3,4,2] => [-1,-2,4,3] => [2]
=> [1,1,0,0,1,0]
=> 1
[-1,3,-4,2] => [-1,-2,-4,-3] => [2]
=> [1,1,0,0,1,0]
=> 1
[1,4,2,3] => [1,4,3,2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[1,4,2,-3] => [1,4,-3,2] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[1,4,-2,3] => [1,-2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,4,-2,-3] => [1,-2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,-4,2,3] => [1,-4,3,-2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[1,-4,2,-3] => [1,-4,-3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[-1,4,2,3] => [-1,-2,4,3] => [2]
=> [1,1,0,0,1,0]
=> 1
[-1,-4,2,3] => [-1,-2,-4,-3] => [2]
=> [1,1,0,0,1,0]
=> 1
[1,4,3,2] => [1,4,3,2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[1,4,3,-2] => [1,-2,4,3] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[1,4,-3,2] => [1,-3,-2,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[1,4,-3,-2] => [1,-2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,-4,3,2] => [1,-4,3,-2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[1,-4,3,-2] => [1,-2,-4,-3] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[1,-4,-3,2] => [1,-3,-2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[-1,4,3,2] => [-1,-2,4,3] => [2]
=> [1,1,0,0,1,0]
=> 1
[-1,-4,3,2] => [-1,-2,-4,-3] => [2]
=> [1,1,0,0,1,0]
=> 1
[2,1,3,4] => [2,1,3,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[2,1,3,-4] => [2,1,3,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[2,1,-3,4] => [2,1,-3,-4] => [2]
=> [1,1,0,0,1,0]
=> 1
[2,1,-3,-4] => [2,1,-3,-4] => [2]
=> [1,1,0,0,1,0]
=> 1
[2,-1,3,4] => [-1,2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[-2,1,3,4] => [-2,-1,3,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[-2,1,3,-4] => [-2,-1,3,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[-2,1,-3,4] => [-2,-1,-3,-4] => [2]
=> [1,1,0,0,1,0]
=> 1
[-2,1,-3,-4] => [-2,-1,-3,-4] => [2]
=> [1,1,0,0,1,0]
=> 1
[2,1,4,3] => [2,1,4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[2,1,4,-3] => [2,1,-3,4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[2,1,-4,3] => [2,1,-4,-3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[2,1,-4,-3] => [2,1,-3,-4] => [2]
=> [1,1,0,0,1,0]
=> 1
[2,-1,4,3] => [-1,2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[-2,1,4,3] => [-2,-1,4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[-2,1,4,-3] => [-2,-1,-3,4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[2,3,1,4] => [3,2,1,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[2,3,1,-4] => [3,2,1,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[2,-3,1,4] => [-3,2,-1,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[2,-3,1,-4] => [-3,2,-1,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[-2,3,1,4] => [-2,-1,3,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[-2,3,1,-4] => [-2,-1,3,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[2,3,4,1] => [4,2,3,1] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[2,3,-4,1] => [-4,2,3,-1] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[2,-3,4,1] => [-3,2,-1,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[2,-3,-4,1] => [-3,2,-1,-4] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
[2,4,1,3] => [4,2,3,1] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> ? = 3
[2,4,1,-3] => [4,2,-3,1] => [2,1]
=> [1,0,1,0,1,0]
=> ? = 2
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
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!