Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000668
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
St000668: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],2)
 => [2]
 => 2
([],3)
 => [3,3]
 => 3
([(1,2)],3)
 => [3]
 => 3
([(0,1),(0,2)],3)
 => [2]
 => 2
([(0,2),(1,2)],3)
 => [2]
 => 2
([(2,3)],4)
 => [4,4,4]
 => 4
([(1,2),(1,3)],4)
 => [8]
 => 8
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => 3
([(0,2),(0,3),(3,1)],4)
 => [3]
 => 3
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => 2
([(1,2),(2,3)],4)
 => [4]
 => 4
([(0,3),(3,1),(3,2)],4)
 => [2]
 => 2
([(1,3),(2,3)],4)
 => [8]
 => 8
([(0,3),(1,3),(3,2)],4)
 => [2]
 => 2
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => 3
([(0,3),(1,2)],4)
 => [4,2]
 => 4
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => 6
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2]
 => 2
([(0,3),(1,2),(2,3)],4)
 => [3]
 => 3
([(0,2),(0,3),(0,4),(4,1)],5)
 => [4,4,4]
 => 4
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [8]
 => 8
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => 3
([(0,3),(0,4),(4,1),(4,2)],5)
 => [8]
 => 8
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => 5
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => 4
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => 6
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2]
 => 2
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => 5
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => 3
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => 5
([(0,4),(1,4),(4,2),(4,3)],5)
 => [2,2]
 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => 6
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => 2
([(0,4),(1,3),(2,3),(3,4)],5)
 => [8]
 => 8
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4,4,4]
 => 4
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => 20
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => 6
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [6]
 => 6
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [2,2]
 => 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => [7]
 => 7
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => 4
([(0,4),(1,2),(1,3),(3,4)],5)
 => [4,4,3]
 => 12
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [3]
 => 3
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [8]
 => 8
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => 6
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => [5,3]
 => 15
([(0,3),(1,2),(1,4),(3,4)],5)
 => [5,4]
 => 20
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => [6]
 => 6
Description
The least common multiple of the parts of the partition.
Matching statistic: St001779
(load all 4 compositions to match this statistic)
Mapping
St001779: Posets ⟶ ℤResult quality: 63% ●values known / values provided: 63%●distinct values known / distinct values provided: 93%
Values
([],2)
 => 2
([],3)
 => 3
([(1,2)],3)
 => 3
([(0,1),(0,2)],3)
 => 2
([(0,2),(1,2)],3)
 => 2
([(2,3)],4)
 => 4
([(1,2),(1,3)],4)
 => 8
([(0,1),(0,2),(0,3)],4)
 => 3
([(0,2),(0,3),(3,1)],4)
 => 3
([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,2),(2,3)],4)
 => 4
([(0,3),(3,1),(3,2)],4)
 => 2
([(1,3),(2,3)],4)
 => 8
([(0,3),(1,3),(3,2)],4)
 => 2
([(0,3),(1,3),(2,3)],4)
 => 3
([(0,3),(1,2)],4)
 => 4
([(0,3),(1,2),(1,3)],4)
 => 6
([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,3),(0,4),(4,1)],5)
 => 4
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 8
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 3
([(0,3),(0,4),(4,1),(4,2)],5)
 => 8
([(1,2),(1,3),(2,4),(3,4)],5)
 => 5
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => 4
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 6
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(1,4),(4,2),(4,3)],5)
 => 5
([(0,4),(4,1),(4,2),(4,3)],5)
 => 3
([(1,4),(2,4),(4,3)],5)
 => 5
([(0,4),(1,4),(4,2),(4,3)],5)
 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 6
([(0,4),(1,4),(2,3),(4,2)],5)
 => 2
([(0,4),(1,3),(2,3),(3,4)],5)
 => 8
([(0,4),(1,4),(2,3),(3,4)],5)
 => 4
([(0,4),(1,2),(1,4),(2,3)],5)
 => 20
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => 6
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => 6
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => 7
([(0,2),(0,4),(3,1),(4,3)],5)
 => 4
([(0,4),(1,2),(1,3),(3,4)],5)
 => 12
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 3
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 8
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => 6
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => 15
([(0,3),(1,2),(1,4),(3,4)],5)
 => 20
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => 6
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
 => ? = 5
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => ? = 3
([(0,2),(0,3),(0,4),(3,6),(4,6),(5,1),(6,5)],7)
 => ? = 12
([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7)
 => ? = 6
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ? = 6
([(0,3),(0,4),(2,5),(3,6),(4,2),(4,6),(6,1),(6,5)],7)
 => ? = 10
([(0,3),(0,5),(3,6),(4,1),(4,6),(5,4),(6,2)],7)
 => ? = 12
([(0,3),(0,4),(2,6),(3,5),(3,6),(4,2),(4,5),(6,1)],7)
 => ? = 24
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7)
 => ? = 15
([(0,4),(0,5),(2,6),(4,2),(5,1),(5,6),(6,3)],7)
 => ? = 9
([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7)
 => ? = 20
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
 => ? = 4
([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7)
 => ? = 4
([(0,2),(0,5),(2,6),(3,4),(4,1),(4,6),(5,3)],7)
 => ? = 20
([(0,5),(1,3),(1,4),(3,6),(4,5),(5,6),(6,2)],7)
 => ? = 12
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
 => ? = 8
([(0,5),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
 => ? = 5
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ? = 2
([(0,6),(1,3),(1,4),(3,5),(4,5),(5,6),(6,2)],7)
 => ? = 5
([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7)
 => ? = 6
([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7)
 => ? = 4
([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7)
 => ? = 6
([(0,3),(0,5),(3,6),(4,2),(5,1),(5,6),(6,4)],7)
 => ? = 20
([(0,4),(0,5),(1,6),(2,6),(5,1),(5,2),(6,3)],7)
 => ? = 12
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)
 => ? = 4
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6),(6,2)],7)
 => ? = 6
([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)
 => ? = 3
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7)
 => ? = 6
([(0,2),(0,5),(2,6),(3,1),(4,3),(4,6),(5,4)],7)
 => ? = 9
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
 => ? = 7
([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,3)],7)
 => ? = 24
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
 => ? = 2
([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
 => ? = 6
([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7)
 => ? = 12
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ? = 20
([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7)
 => ? = 24
([(0,5),(2,6),(4,1),(4,6),(5,2),(5,4),(6,3)],7)
 => ? = 7
([(0,5),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4)],7)
 => ? = 20
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 6
([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7)
 => ? = 12
([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
 => ? = 4
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7)
 => ? = 6
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7)
 => ? = 2
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)
 => ? = 2
([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7)
 => ? = 7
([(0,5),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ? = 5
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => ? = 3
([(0,6),(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)
 => ? = 5
([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7)
 => ? = 3
([(0,5),(1,4),(4,6),(5,6),(6,2),(6,3)],7)
 => ? = 4
Description
The order of promotion on the set of linear extensions of a poset.
Matching statistic: St001491
(load all 2 compositions to match this statistic)
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St001491: Binary words ⟶ ℤResult quality: 14% ●values known / values provided: 17%●distinct values known / distinct values provided: 14%
Values
([],2)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([],3)
 => [3,3]
 => [2,2,2]
 => 11100 => ? = 3 - 1
([(1,2)],3)
 => [3]
 => [1,1,1]
 => 1110 => 2 = 3 - 1
([(0,1),(0,2)],3)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([(0,2),(1,2)],3)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([(2,3)],4)
 => [4,4,4]
 => [3,3,3,3]
 => 1111000 => ? = 4 - 1
([(1,2),(1,3)],4)
 => [8]
 => [1,1,1,1,1,1,1,1]
 => 111111110 => ? = 8 - 1
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [2,2,2]
 => 11100 => ? = 3 - 1
([(0,2),(0,3),(3,1)],4)
 => [3]
 => [1,1,1]
 => 1110 => 2 = 3 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([(1,2),(2,3)],4)
 => [4]
 => [1,1,1,1]
 => 11110 => ? = 4 - 1
([(0,3),(3,1),(3,2)],4)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => [8]
 => [1,1,1,1,1,1,1,1]
 => 111111110 => ? = 8 - 1
([(0,3),(1,3),(3,2)],4)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [2,2,2]
 => 11100 => ? = 3 - 1
([(0,3),(1,2)],4)
 => [4,2]
 => [2,2,1,1]
 => 110110 => ? = 4 - 1
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => [2,2,1]
 => 11010 => ? = 6 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => [1,1,1]
 => 1110 => 2 = 3 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => [4,4,4]
 => [3,3,3,3]
 => 1111000 => ? = 4 - 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1]
 => 111111110 => ? = 8 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [2,2,2]
 => 11100 => ? = 3 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => [8]
 => [1,1,1,1,1,1,1,1]
 => 111111110 => ? = 8 - 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => [2,2,2,2,2]
 => 1111100 => ? = 5 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => [2,2,1,1]
 => 110110 => ? = 4 - 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => [2,2,1]
 => 11010 => ? = 6 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => [2,2,2,2,2]
 => 1111100 => ? = 5 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => [2,2,2]
 => 11100 => ? = 3 - 1
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => [2,2,2,2,2]
 => 1111100 => ? = 5 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => [2,2,2]
 => 11100 => ? = 3 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [2,2,2,2,2,2]
 => 11111100 => ? = 6 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1]
 => 111111110 => ? = 8 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4,4,4]
 => [3,3,3,3]
 => 1111000 => ? = 4 - 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => [2,2,2,2,1]
 => 1111010 => ? = 20 - 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => [2,2,1]
 => 11010 => ? = 6 - 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [6]
 => [1,1,1,1,1,1]
 => 1111110 => ? = 6 - 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => [7]
 => [1,1,1,1,1,1,1]
 => 11111110 => ? = 7 - 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => [1,1,1,1]
 => 11110 => ? = 4 - 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => [4,4,3]
 => [3,3,3,2]
 => 1110100 => ? = 12 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [3]
 => [1,1,1]
 => 1110 => 2 = 3 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1]
 => 111111110 => ? = 8 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [2,2,2,2,2,2]
 => 11111100 => ? = 6 - 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => [5,3]
 => [2,2,2,1,1]
 => 1110110 => ? = 15 - 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => [5,4]
 => [2,2,2,2,1]
 => 1111010 => ? = 20 - 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => [6]
 => [1,1,1,1,1,1]
 => 1111110 => ? = 6 - 1
([(1,4),(3,2),(4,3)],5)
 => [5]
 => [1,1,1,1,1]
 => 111110 => ? = 5 - 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => [3]
 => [1,1,1]
 => 1110 => 2 = 3 - 1
([(0,3),(1,4),(4,2)],5)
 => [5,5]
 => [2,2,2,2,2]
 => 1111100 => ? = 5 - 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => [3]
 => [1,1,1]
 => 1110 => 2 = 3 - 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => [7]
 => [1,1,1,1,1,1,1]
 => 11111110 => ? = 7 - 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,2]
 => [2,2,1,1]
 => 110110 => ? = 4 - 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => [1,1,1,1]
 => 11110 => ? = 4 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [2,2,2]
 => 11100 => ? = 3 - 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,6]
 => [2,2,2,2,2,2]
 => 11111100 => ? = 6 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => [8]
 => [1,1,1,1,1,1,1,1]
 => 111111110 => ? = 8 - 1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,5]
 => [2,2,2,2,2]
 => 1111100 => ? = 5 - 1
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => [12]
 => [1,1,1,1,1,1,1,1,1,1,1,1]
 => 1111111111110 => ? = 12 - 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
 => [6]
 => [1,1,1,1,1,1]
 => 1111110 => ? = 6 - 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => [7]
 => [1,1,1,1,1,1,1]
 => 11111110 => ? = 7 - 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => [6,6]
 => [2,2,2,2,2,2]
 => 11111100 => ? = 6 - 1
([(1,4),(4,5),(5,2),(5,3)],6)
 => [12]
 => [1,1,1,1,1,1,1,1,1,1,1,1]
 => 1111111111110 => ? = 12 - 1
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
 => [3,3]
 => [2,2,2]
 => 11100 => ? = 3 - 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
 => [6,6]
 => [2,2,2,2,2,2]
 => 11111100 => ? = 6 - 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => [3]
 => [1,1,1]
 => 1110 => 2 = 3 - 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
 => [3]
 => [1,1,1]
 => 1110 => 2 = 3 - 1
([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => [3]
 => [1,1,1]
 => 1110 => 2 = 3 - 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => [3]
 => [1,1,1]
 => 1110 => 2 = 3 - 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => [2]
 => [1,1]
 => 110 => 1 = 2 - 1
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => [3]
 => [1,1,1]
 => 1110 => 2 = 3 - 1
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
 => [3]
 => [1,1,1]
 => 1110 => 2 = 3 - 1
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)
 => [2,2]
 => [2,2]
 => 1100 => 1 = 2 - 1
Description
The number of indecomposable projective-injective modules in the algebra corresponding to a subset. Let $A_n=K[x]/(x^n)$. We associate to a nonempty subset S of an (n-1)-set the module $M_S$, which is the direct sum of $A_n$-modules with indecomposable non-projective direct summands of dimension $i$ when $i$ is in $S$ (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of $M_S$. We decode the subset as a binary word so that for example the subset $S=\{1,3 \} $ of $\{1,2,3 \}$ is decoded as 101.