Your data matches 130 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000993
(load all 3 compositions to match this statistic)
Mapping
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000993: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [2]
 => [1,1]
 => 2
([],2)
 => [2,2]
 => [2,2]
 => 2
([(0,1)],2)
 => [3]
 => [1,1,1]
 => 3
([],3)
 => [2,2,2,2]
 => [4,4]
 => 2
([(1,2)],3)
 => [6]
 => [1,1,1,1,1,1]
 => 6
([(0,1),(0,2)],3)
 => [3,2]
 => [2,2,1]
 => 2
([(0,2),(2,1)],3)
 => [4]
 => [1,1,1,1]
 => 4
([(0,2),(1,2)],3)
 => [3,2]
 => [2,2,1]
 => 2
([(0,1),(0,2),(0,3)],4)
 => [3,2,2,2]
 => [4,4,1]
 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [4,2]
 => [2,2,1,1]
 => 2
([(1,2),(2,3)],4)
 => [4,4]
 => [2,2,2,2]
 => 4
([(0,3),(3,1),(3,2)],4)
 => [4,2]
 => [2,2,1,1]
 => 2
([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => [2,2,1,1]
 => 2
([(0,3),(1,3),(2,3)],4)
 => [3,2,2,2]
 => [4,4,1]
 => 2
([(0,3),(1,2)],4)
 => [3,3,3]
 => [3,3,3]
 => 3
([(0,3),(1,2),(1,3)],4)
 => [5,3]
 => [2,2,2,1,1]
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => [3,2,2]
 => [3,3,1]
 => 2
([(0,3),(2,1),(3,2)],4)
 => [5]
 => [1,1,1,1,1]
 => 5
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [5,2]
 => [2,2,1,1,1]
 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,3,3]
 => [3,3,3,1]
 => 3
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [5,4]
 => [2,2,2,2,1]
 => 4
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [4,2,2]
 => [3,3,1,1]
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => [4,2,2]
 => [3,3,1,1]
 => 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [5,2]
 => [2,2,1,1,1]
 => 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [5,4]
 => [2,2,2,2,1]
 => 4
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [4,2,2]
 => [3,3,1,1]
 => 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [5,4]
 => [2,2,2,2,1]
 => 4
([(0,3),(3,4),(4,1),(4,2)],5)
 => [5,2]
 => [2,2,1,1,1]
 => 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [6]
 => [1,1,1,1,1,1]
 => 6
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,3,3]
 => [3,3,3,1]
 => 3
([(0,4),(1,2),(2,3),(3,4)],5)
 => [5,4]
 => [2,2,2,2,1]
 => 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [5,2]
 => [2,2,1,1,1]
 => 2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [5,5]
 => [2,2,2,2,2]
 => 5
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [5,5]
 => [2,2,2,2,2]
 => 5
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [5,5]
 => [2,2,2,2,2]
 => 5
Description
The multiplicity of the largest part of an integer partition.
Matching statistic: St001038
(load all 2 compositions to match this statistic)
Mapping
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001038: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [2]
 => [1,0,1,0]
 => 2
([],2)
 => [2,2]
 => [1,1,1,0,0,0]
 => 2
([(0,1)],2)
 => [3]
 => [1,0,1,0,1,0]
 => 3
([],3)
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => 2
([(1,2)],3)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 6
([(0,1),(0,2)],3)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => 2
([(0,2),(2,1)],3)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => 4
([(0,2),(1,2)],3)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => 2
([(0,1),(0,2),(0,3)],4)
 => [3,2,2,2]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => 2
([(1,2),(2,3)],4)
 => [4,4]
 => [1,1,1,0,1,0,1,0,0,0]
 => 4
([(0,3),(3,1),(3,2)],4)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => 2
([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => 2
([(0,3),(1,3),(2,3)],4)
 => [3,2,2,2]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => 2
([(0,3),(1,2)],4)
 => [3,3,3]
 => [1,1,1,1,1,0,0,0,0,0]
 => 3
([(0,3),(1,2),(1,3)],4)
 => [5,3]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 2
([(0,3),(2,1),(3,2)],4)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => 5
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,3,3]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 3
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => 4
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => 4
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => 4
([(0,3),(3,4),(4,1),(4,2)],5)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 6
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,3,3]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 3
([(0,4),(1,2),(2,3),(3,4)],5)
 => [5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => 2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [5,5]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => 5
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [5,5]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => 5
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [5,5]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => 5
Description
The minimal height of a column in the parallelogram polyomino associated with the Dyck path.
Matching statistic: St000297
Mapping
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St000297: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [2]
 => [1,1]
 => 110 => 2
([],2)
 => [2,2]
 => [2,2]
 => 1100 => 2
([(0,1)],2)
 => [3]
 => [1,1,1]
 => 1110 => 3
([],3)
 => [2,2,2,2]
 => [4,4]
 => 110000 => 2
([(1,2)],3)
 => [6]
 => [1,1,1,1,1,1]
 => 1111110 => 6
([(0,1),(0,2)],3)
 => [3,2]
 => [2,2,1]
 => 11010 => 2
([(0,2),(2,1)],3)
 => [4]
 => [1,1,1,1]
 => 11110 => 4
([(0,2),(1,2)],3)
 => [3,2]
 => [2,2,1]
 => 11010 => 2
([(0,1),(0,2),(0,3)],4)
 => [3,2,2,2]
 => [4,4,1]
 => 1100010 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [4,2]
 => [2,2,1,1]
 => 110110 => 2
([(1,2),(2,3)],4)
 => [4,4]
 => [2,2,2,2]
 => 111100 => 4
([(0,3),(3,1),(3,2)],4)
 => [4,2]
 => [2,2,1,1]
 => 110110 => 2
([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => [2,2,1,1]
 => 110110 => 2
([(0,3),(1,3),(2,3)],4)
 => [3,2,2,2]
 => [4,4,1]
 => 1100010 => 2
([(0,3),(1,2)],4)
 => [3,3,3]
 => [3,3,3]
 => 111000 => 3
([(0,3),(1,2),(1,3)],4)
 => [5,3]
 => [2,2,2,1,1]
 => 1110110 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => [3,2,2]
 => [3,3,1]
 => 110010 => 2
([(0,3),(2,1),(3,2)],4)
 => [5]
 => [1,1,1,1,1]
 => 111110 => 5
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [5,2]
 => [2,2,1,1,1]
 => 1101110 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,3,3]
 => [3,3,3,1]
 => 1110010 => 3
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [5,4]
 => [2,2,2,2,1]
 => 1111010 => 4
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [4,2,2]
 => [3,3,1,1]
 => 1100110 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => [4,2,2]
 => [3,3,1,1]
 => 1100110 => 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [5,2]
 => [2,2,1,1,1]
 => 1101110 => 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [5,4]
 => [2,2,2,2,1]
 => 1111010 => 4
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [4,2,2]
 => [3,3,1,1]
 => 1100110 => 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [5,4]
 => [2,2,2,2,1]
 => 1111010 => 4
([(0,3),(3,4),(4,1),(4,2)],5)
 => [5,2]
 => [2,2,1,1,1]
 => 1101110 => 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [6]
 => [1,1,1,1,1,1]
 => 1111110 => 6
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,3,3]
 => [3,3,3,1]
 => 1110010 => 3
([(0,4),(1,2),(2,3),(3,4)],5)
 => [5,4]
 => [2,2,2,2,1]
 => 1111010 => 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [5,2]
 => [2,2,1,1,1]
 => 1101110 => 2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [5,5]
 => [2,2,2,2,2]
 => 1111100 => 5
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [5,5]
 => [2,2,2,2,2]
 => 1111100 => 5
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [5,5]
 => [2,2,2,2,2]
 => 1111100 => 5
Description
The number of leading ones in a binary word.
Matching statistic: St000617
Mapping
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
St000617: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
([],2)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,1,0,0]
 => 2
([(0,1)],2)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 3
([],3)
 => [2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => 2
([(1,2)],3)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => 6
([(0,1),(0,2)],3)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 2
([(0,2),(2,1)],3)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 4
([(0,2),(1,2)],3)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 2
([(0,1),(0,2),(0,3)],4)
 => [3,2,2,2]
 => [1,1,0,0,1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => 2
([(1,2),(2,3)],4)
 => [4,4]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => 4
([(0,3),(3,1),(3,2)],4)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => 2
([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => 2
([(0,3),(1,3),(2,3)],4)
 => [3,2,2,2]
 => [1,1,0,0,1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => 2
([(0,3),(1,2)],4)
 => [3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => 3
([(0,3),(1,2),(1,3)],4)
 => [5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 2
([(0,3),(2,1),(3,2)],4)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 5
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,3,3]
 => [1,1,1,0,0,0,1,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => 3
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => 4
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => [4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => 4
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => 4
([(0,3),(3,4),(4,1),(4,2)],5)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => 6
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,3,3]
 => [1,1,1,0,0,0,1,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => 3
([(0,4),(1,2),(2,3),(3,4)],5)
 => [5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => 2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => 5
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => 5
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => 5
Description
The number of global maxima of a Dyck path.
Matching statistic: St000733
(load all 2 compositions to match this statistic)
Mapping
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
St000733: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [2]
 => [1,1]
 => [[1],[2]]
 => 2
([],2)
 => [2,2]
 => [2,2]
 => [[1,2],[3,4]]
 => 2
([(0,1)],2)
 => [3]
 => [1,1,1]
 => [[1],[2],[3]]
 => 3
([],3)
 => [2,2,2,2]
 => [4,4]
 => [[1,2,3,4],[5,6,7,8]]
 => 2
([(1,2)],3)
 => [6]
 => [1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6]]
 => 6
([(0,1),(0,2)],3)
 => [3,2]
 => [2,2,1]
 => [[1,3],[2,5],[4]]
 => 2
([(0,2),(2,1)],3)
 => [4]
 => [1,1,1,1]
 => [[1],[2],[3],[4]]
 => 4
([(0,2),(1,2)],3)
 => [3,2]
 => [2,2,1]
 => [[1,3],[2,5],[4]]
 => 2
([(0,1),(0,2),(0,3)],4)
 => [3,2,2,2]
 => [4,4,1]
 => [[1,3,4,5],[2,7,8,9],[6]]
 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [4,2]
 => [2,2,1,1]
 => [[1,4],[2,6],[3],[5]]
 => 2
([(1,2),(2,3)],4)
 => [4,4]
 => [2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8]]
 => 4
([(0,3),(3,1),(3,2)],4)
 => [4,2]
 => [2,2,1,1]
 => [[1,4],[2,6],[3],[5]]
 => 2
([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => [2,2,1,1]
 => [[1,4],[2,6],[3],[5]]
 => 2
([(0,3),(1,3),(2,3)],4)
 => [3,2,2,2]
 => [4,4,1]
 => [[1,3,4,5],[2,7,8,9],[6]]
 => 2
([(0,3),(1,2)],4)
 => [3,3,3]
 => [3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9]]
 => 3
([(0,3),(1,2),(1,3)],4)
 => [5,3]
 => [2,2,2,1,1]
 => [[1,4],[2,6],[3,8],[5],[7]]
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => [3,2,2]
 => [3,3,1]
 => [[1,3,4],[2,6,7],[5]]
 => 2
([(0,3),(2,1),(3,2)],4)
 => [5]
 => [1,1,1,1,1]
 => [[1],[2],[3],[4],[5]]
 => 5
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [5,2]
 => [2,2,1,1,1]
 => [[1,5],[2,7],[3],[4],[6]]
 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,3,3]
 => [3,3,3,1]
 => [[1,3,4],[2,6,7],[5,9,10],[8]]
 => 3
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [5,4]
 => [2,2,2,2,1]
 => [[1,3],[2,5],[4,7],[6,9],[8]]
 => 4
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [4,2,2]
 => [3,3,1,1]
 => [[1,4,5],[2,7,8],[3],[6]]
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => [4,2,2]
 => [3,3,1,1]
 => [[1,4,5],[2,7,8],[3],[6]]
 => 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [5,2]
 => [2,2,1,1,1]
 => [[1,5],[2,7],[3],[4],[6]]
 => 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [5,4]
 => [2,2,2,2,1]
 => [[1,3],[2,5],[4,7],[6,9],[8]]
 => 4
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [4,2,2]
 => [3,3,1,1]
 => [[1,4,5],[2,7,8],[3],[6]]
 => 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [5,4]
 => [2,2,2,2,1]
 => [[1,3],[2,5],[4,7],[6,9],[8]]
 => 4
([(0,3),(3,4),(4,1),(4,2)],5)
 => [5,2]
 => [2,2,1,1,1]
 => [[1,5],[2,7],[3],[4],[6]]
 => 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [6]
 => [1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6]]
 => 6
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,3,3]
 => [3,3,3,1]
 => [[1,3,4],[2,6,7],[5,9,10],[8]]
 => 3
([(0,4),(1,2),(2,3),(3,4)],5)
 => [5,4]
 => [2,2,2,2,1]
 => [[1,3],[2,5],[4,7],[6,9],[8]]
 => 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [5,2]
 => [2,2,1,1,1]
 => [[1,5],[2,7],[3],[4],[6]]
 => 2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [5,5]
 => [2,2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8],[9,10]]
 => 5
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [5,5]
 => [2,2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8],[9,10]]
 => 5
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [5,5]
 => [2,2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8],[9,10]]
 => 5
Description
The row containing the largest entry of a standard tableau.
Matching statistic: St000745
Mapping
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
St000745: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [2]
 => [[1,2]]
 => [[1],[2]]
 => 2
([],2)
 => [2,2]
 => [[1,2],[3,4]]
 => [[1,3],[2,4]]
 => 2
([(0,1)],2)
 => [3]
 => [[1,2,3]]
 => [[1],[2],[3]]
 => 3
([],3)
 => [2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8]]
 => [[1,3,5,7],[2,4,6,8]]
 => 2
([(1,2)],3)
 => [6]
 => [[1,2,3,4,5,6]]
 => [[1],[2],[3],[4],[5],[6]]
 => 6
([(0,1),(0,2)],3)
 => [3,2]
 => [[1,2,5],[3,4]]
 => [[1,3],[2,4],[5]]
 => 2
([(0,2),(2,1)],3)
 => [4]
 => [[1,2,3,4]]
 => [[1],[2],[3],[4]]
 => 4
([(0,2),(1,2)],3)
 => [3,2]
 => [[1,2,5],[3,4]]
 => [[1,3],[2,4],[5]]
 => 2
([(0,1),(0,2),(0,3)],4)
 => [3,2,2,2]
 => [[1,2,9],[3,4],[5,6],[7,8]]
 => [[1,3,5,7],[2,4,6,8],[9]]
 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [4,2]
 => [[1,2,5,6],[3,4]]
 => [[1,3],[2,4],[5],[6]]
 => 2
([(1,2),(2,3)],4)
 => [4,4]
 => [[1,2,3,4],[5,6,7,8]]
 => [[1,5],[2,6],[3,7],[4,8]]
 => 4
([(0,3),(3,1),(3,2)],4)
 => [4,2]
 => [[1,2,5,6],[3,4]]
 => [[1,3],[2,4],[5],[6]]
 => 2
([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => [[1,2,5,6],[3,4]]
 => [[1,3],[2,4],[5],[6]]
 => 2
([(0,3),(1,3),(2,3)],4)
 => [3,2,2,2]
 => [[1,2,9],[3,4],[5,6],[7,8]]
 => [[1,3,5,7],[2,4,6,8],[9]]
 => 2
([(0,3),(1,2)],4)
 => [3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9]]
 => [[1,4,7],[2,5,8],[3,6,9]]
 => 3
([(0,3),(1,2),(1,3)],4)
 => [5,3]
 => [[1,2,3,7,8],[4,5,6]]
 => [[1,4],[2,5],[3,6],[7],[8]]
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => [3,2,2]
 => [[1,2,7],[3,4],[5,6]]
 => [[1,3,5],[2,4,6],[7]]
 => 2
([(0,3),(2,1),(3,2)],4)
 => [5]
 => [[1,2,3,4,5]]
 => [[1],[2],[3],[4],[5]]
 => 5
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [5,2]
 => [[1,2,5,6,7],[3,4]]
 => [[1,3],[2,4],[5],[6],[7]]
 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,3,3]
 => [[1,2,3,10],[4,5,6],[7,8,9]]
 => [[1,4,7],[2,5,8],[3,6,9],[10]]
 => 3
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [5,4]
 => [[1,2,3,4,9],[5,6,7,8]]
 => [[1,5],[2,6],[3,7],[4,8],[9]]
 => 4
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [4,2,2]
 => [[1,2,7,8],[3,4],[5,6]]
 => [[1,3,5],[2,4,6],[7],[8]]
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => [4,2,2]
 => [[1,2,7,8],[3,4],[5,6]]
 => [[1,3,5],[2,4,6],[7],[8]]
 => 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [5,2]
 => [[1,2,5,6,7],[3,4]]
 => [[1,3],[2,4],[5],[6],[7]]
 => 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [5,4]
 => [[1,2,3,4,9],[5,6,7,8]]
 => [[1,5],[2,6],[3,7],[4,8],[9]]
 => 4
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [4,2,2]
 => [[1,2,7,8],[3,4],[5,6]]
 => [[1,3,5],[2,4,6],[7],[8]]
 => 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [5,4]
 => [[1,2,3,4,9],[5,6,7,8]]
 => [[1,5],[2,6],[3,7],[4,8],[9]]
 => 4
([(0,3),(3,4),(4,1),(4,2)],5)
 => [5,2]
 => [[1,2,5,6,7],[3,4]]
 => [[1,3],[2,4],[5],[6],[7]]
 => 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [6]
 => [[1,2,3,4,5,6]]
 => [[1],[2],[3],[4],[5],[6]]
 => 6
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,3,3]
 => [[1,2,3,10],[4,5,6],[7,8,9]]
 => [[1,4,7],[2,5,8],[3,6,9],[10]]
 => 3
([(0,4),(1,2),(2,3),(3,4)],5)
 => [5,4]
 => [[1,2,3,4,9],[5,6,7,8]]
 => [[1,5],[2,6],[3,7],[4,8],[9]]
 => 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [5,2]
 => [[1,2,5,6,7],[3,4]]
 => [[1,3],[2,4],[5],[6],[7]]
 => 2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [5,5]
 => [[1,2,3,4,5],[6,7,8,9,10]]
 => [[1,6],[2,7],[3,8],[4,9],[5,10]]
 => 5
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [5,5]
 => [[1,2,3,4,5],[6,7,8,9,10]]
 => [[1,6],[2,7],[3,8],[4,9],[5,10]]
 => 5
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [5,5]
 => [[1,2,3,4,5],[6,7,8,9,10]]
 => [[1,6],[2,7],[3,8],[4,9],[5,10]]
 => 5
Description
The index of the last row whose first entry is the row number in a standard Young tableau.
Matching statistic: St001184
Mapping
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001184: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 2
([],2)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => 2
([(0,1)],2)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 3
([],3)
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 2
([(1,2)],3)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 6
([(0,1),(0,2)],3)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
([(0,2),(2,1)],3)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 4
([(0,2),(1,2)],3)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
([(0,1),(0,2),(0,3)],4)
 => [3,2,2,2]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
([(1,2),(2,3)],4)
 => [4,4]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
([(0,3),(3,1),(3,2)],4)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
([(0,3),(1,3),(2,3)],4)
 => [3,2,2,2]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => 2
([(0,3),(1,2)],4)
 => [3,3,3]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => 3
([(0,3),(1,2),(1,3)],4)
 => [5,3]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => 2
([(0,3),(2,1),(3,2)],4)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 5
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,3,3]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 3
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
([(0,3),(3,4),(4,1),(4,2)],5)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 6
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,3,3]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 3
([(0,4),(1,2),(2,3),(3,4)],5)
 => [5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [5,5]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [5,5]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [5,5]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
Description
Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra.
Matching statistic: St001481
Mapping
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001481: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 2
([],2)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => 2
([(0,1)],2)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 3
([],3)
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 2
([(1,2)],3)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 6
([(0,1),(0,2)],3)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
([(0,2),(2,1)],3)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 4
([(0,2),(1,2)],3)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
([(0,1),(0,2),(0,3)],4)
 => [3,2,2,2]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
([(1,2),(2,3)],4)
 => [4,4]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
([(0,3),(3,1),(3,2)],4)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
([(0,3),(1,3),(2,3)],4)
 => [3,2,2,2]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => 2
([(0,3),(1,2)],4)
 => [3,3,3]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => 3
([(0,3),(1,2),(1,3)],4)
 => [5,3]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => 2
([(0,3),(2,1),(3,2)],4)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 5
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,3,3]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 3
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
([(0,3),(3,4),(4,1),(4,2)],5)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 6
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,3,3]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 3
([(0,4),(1,2),(2,3),(3,4)],5)
 => [5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [5,5]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [5,5]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [5,5]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
Description
The minimal height of a peak of a Dyck path.
Matching statistic: St000326
Mapping
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
St000326: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [2]
 => 100 => 001 => 3 = 2 + 1
([],2)
 => [2,2]
 => 1100 => 0011 => 3 = 2 + 1
([(0,1)],2)
 => [3]
 => 1000 => 0001 => 4 = 3 + 1
([],3)
 => [2,2,2,2]
 => 111100 => 001111 => 3 = 2 + 1
([(1,2)],3)
 => [6]
 => 1000000 => 0000001 => 7 = 6 + 1
([(0,1),(0,2)],3)
 => [3,2]
 => 10100 => 00101 => 3 = 2 + 1
([(0,2),(2,1)],3)
 => [4]
 => 10000 => 00001 => 5 = 4 + 1
([(0,2),(1,2)],3)
 => [3,2]
 => 10100 => 00101 => 3 = 2 + 1
([(0,1),(0,2),(0,3)],4)
 => [3,2,2,2]
 => 1011100 => 0011101 => 3 = 2 + 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => [4,2]
 => 100100 => 001001 => 3 = 2 + 1
([(1,2),(2,3)],4)
 => [4,4]
 => 110000 => 000011 => 5 = 4 + 1
([(0,3),(3,1),(3,2)],4)
 => [4,2]
 => 100100 => 001001 => 3 = 2 + 1
([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => 100100 => 001001 => 3 = 2 + 1
([(0,3),(1,3),(2,3)],4)
 => [3,2,2,2]
 => 1011100 => 0011101 => 3 = 2 + 1
([(0,3),(1,2)],4)
 => [3,3,3]
 => 111000 => 000111 => 4 = 3 + 1
([(0,3),(1,2),(1,3)],4)
 => [5,3]
 => 1001000 => 0001001 => 4 = 3 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [3,2,2]
 => 101100 => 001101 => 3 = 2 + 1
([(0,3),(2,1),(3,2)],4)
 => [5]
 => 100000 => 000001 => 6 = 5 + 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [5,2]
 => 1000100 => 0010001 => 3 = 2 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,3,3]
 => 1011000 => 0001101 => 4 = 3 + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [5,4]
 => 1010000 => 0000101 => 5 = 4 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [4,2,2]
 => 1001100 => 0011001 => 3 = 2 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => [4,2,2]
 => 1001100 => 0011001 => 3 = 2 + 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => [5,2]
 => 1000100 => 0010001 => 3 = 2 + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [5,4]
 => 1010000 => 0000101 => 5 = 4 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [4,2,2]
 => 1001100 => 0011001 => 3 = 2 + 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => [5,4]
 => 1010000 => 0000101 => 5 = 4 + 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => [5,2]
 => 1000100 => 0010001 => 3 = 2 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => [6]
 => 1000000 => 0000001 => 7 = 6 + 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,3,3]
 => 1011000 => 0001101 => 4 = 3 + 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => [5,4]
 => 1010000 => 0000101 => 5 = 4 + 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [5,2]
 => 1000100 => 0010001 => 3 = 2 + 1
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [5,5]
 => 1100000 => 0000011 => 6 = 5 + 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [5,5]
 => 1100000 => 0000011 => 6 = 5 + 1
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [5,5]
 => 1100000 => 0000011 => 6 = 5 + 1
Description
The position of the first one in a binary word after appending a 1 at the end. Regarding the binary word as a subset of $\{1,\dots,n,n+1\}$ that contains $n+1$, this is the minimal element of the set.
Matching statistic: St000642
(load all 2 compositions to match this statistic)
Mapping
St000642: Posets ⟶ ℤResult quality: 97% ●values known / values provided: 97%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ? = 2
([],2)
 => 2
([(0,1)],2)
 => 3
([],3)
 => 2
([(1,2)],3)
 => 6
([(0,1),(0,2)],3)
 => 2
([(0,2),(2,1)],3)
 => 4
([(0,2),(1,2)],3)
 => 2
([(0,1),(0,2),(0,3)],4)
 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,2),(2,3)],4)
 => 4
([(0,3),(3,1),(3,2)],4)
 => 2
([(0,3),(1,3),(3,2)],4)
 => 2
([(0,3),(1,3),(2,3)],4)
 => 2
([(0,3),(1,2)],4)
 => 3
([(0,3),(1,2),(1,3)],4)
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,3),(2,1),(3,2)],4)
 => 5
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => 3
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 4
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => 4
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => 4
([(0,3),(3,4),(4,1),(4,2)],5)
 => 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => 6
([(0,3),(1,2),(2,4),(3,4)],5)
 => 3
([(0,4),(1,2),(2,3),(3,4)],5)
 => 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => 5
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 5
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => 5
Description
The size of the smallest orbit of antichains under Panyushev complementation.
The following 120 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St000474Dyson's crank of a partition. St000667The greatest common divisor of the parts of the partition. St000668The least common multiple of the parts of the partition. St000770The major index of an integer partition when read from bottom to top. St001571The Cartan determinant of the integer partition. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001933The largest multiplicity of a part in an integer partition. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St001645The pebbling number of a connected graph. St000259The diameter of a connected graph. St000260The radius of a connected graph. St000302The determinant of the distance matrix of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St000467The hyper-Wiener index of a connected graph. St000455The second largest eigenvalue of a graph if it is integral. St001330The hat guessing number of a graph. St000264The girth of a graph, which is not a tree. St000464The Schultz index of a connected graph. St001545The second Elser number of a connected graph. St000456The monochromatic index of a connected graph. St001060The distinguishing index of a graph. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001570The minimal number of edges to add to make a graph Hamiltonian. St000046The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St000137The Grundy value of an integer partition. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000460The hook length of the last cell along the main diagonal of an integer partition. St000618The number of self-evacuating tableaux of given shape. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000781The number of proper colouring schemes of a Ferrers diagram. St000870The product of the hook lengths of the diagonal cells in an integer partition. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a partition. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001262The dimension of the maximal parabolic seaweed algebra corresponding to the partition. St001283The number of finite solvable groups that are realised by the given partition over the complex numbers. St001284The number of finite groups that are realised by the given partition over the complex numbers. St001360The number of covering relations in Young's lattice below a partition. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St001378The product of the cohook lengths of the integer partition. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001383The BG-rank of an integer partition. St001389The number of partitions of the same length below the given integer partition. St001432The order dimension of the partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001525The number of symmetric hooks on the diagonal of a partition. St001527The cyclic permutation representation number of an integer partition. St001529The number of monomials in the expansion of the nabla operator applied to the power-sum symmetric function indexed by the partition. St001561The value of the elementary symmetric function evaluated at 1. St001562The value of the complete homogeneous symmetric function evaluated at 1. St001563The value of the power-sum symmetric function evaluated at 1. St001564The value of the forgotten symmetric functions when all variables set to 1. St001593This is the number of standard Young tableaux of the given shifted shape. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001602The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on endofunctions. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001607The number of coloured graphs such that the multiplicities of colours are given by a partition. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001610The number of coloured endofunctions such that the multiplicities of colours are given by a partition. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. St001627The number of coloured connected graphs such that the multiplicities of colours are given by a partition. St001628The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001763The Hurwitz number of an integer partition. St001780The order of promotion on the set of standard tableaux of given shape. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001924The number of cells in an integer partition whose arm and leg length coincide. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St001938The number of transitive monotone factorizations of genus zero of a permutation of given cycle type. St001939The number of parts that are equal to their multiplicity in the integer partition. St001940The number of distinct parts that are equal to their multiplicity in the integer partition. St001943The sum of the squares of the hook lengths of an integer partition. St000145The Dyson rank of a partition. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000225Difference between largest and smallest parts in a partition. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000749The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree. St000944The 3-degree of an integer partition. St001118The acyclic chromatic index of a graph. St001175The size of a partition minus the hook length of the base cell. St001176The size of a partition minus its first part. St001177Twice the mean value of the major index among all standard Young tableaux of a partition. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. St001248Sum of the even parts of a partition. St001279The sum of the parts of an integer partition that are at least two. St001280The number of parts of an integer partition that are at least two. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001541The Gini index of an integer partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St001587Half of the largest even part of an integer partition. St001657The number of twos in an integer partition. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St001961The sum of the greatest common divisors of all pairs of parts.