Your data matches 8 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001570
Mapping
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00156: Graphs —line graph⟶ Graphs
Mp00157: Graphs —connected complement⟶ Graphs
St001570: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 0
([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
([(0,1),(0,2),(0,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 0
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 0
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 0
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 0
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 0
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 0
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 2
([(1,4),(3,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
([(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0
([(0,3),(1,4),(4,2)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => 0
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0
Description
The minimal number of edges to add to make a graph Hamiltonian. A graph is Hamiltonian if it contains a cycle as a subgraph, which contains all vertices.
Matching statistic: St000689
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00229: Dyck paths —Delest-Viennot⟶ Dyck paths
St000689: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 50%
Values
([],3)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 0
([],4)
 => [4,4,4,4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(2,3)],4)
 => [4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 0
([(1,2),(1,3)],4)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 0
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 0
([(1,2),(2,3)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => 0
([(1,3),(2,3)],4)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 0
([(0,3),(1,2)],4)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 0
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(0,2),(0,3),(0,4),(4,1)],5)
 => [4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 0
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 0
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 0
([(1,3),(1,4),(4,2)],5)
 => [15]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 0
([(0,3),(0,4),(4,1),(4,2)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 0
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 0
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 0
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => 1
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 0
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 0
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 0
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
 => ? = 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 2
([(0,4),(1,3),(2,3),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 0
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
 => ? = 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 0
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
 => ? = 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => 0
([(0,4),(1,2),(1,3),(3,4)],5)
 => [4,4,3]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => ? = 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 0
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => [5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => ? = 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => [5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2
([(1,4),(3,2),(4,3)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 0
([(1,4),(2,3),(3,4)],5)
 => [15]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 0
([(0,3),(1,4),(4,2)],5)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 0
([(0,4),(1,2),(2,3),(2,4)],5)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 0
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => 0
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,4,4,4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 0
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
 => [12,4]
 => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
 => ? = 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [14]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
 => [10,4,4]
 => [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
 => ? = 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 0
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 0
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,5,5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 2
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => [12]
 => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 0
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
 => [10,4,4]
 => [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
 => ? = 2
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
 => [12,4]
 => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
 => ? = 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
 => [14]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 0
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 0
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 0
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 0
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => 0
([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 0
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => 0
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => 0
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => 1
([(0,5),(3,2),(4,1),(5,3),(5,4)],6)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 0
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 0
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 0
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 0
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => 1
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => 0
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 0
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => 1
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 0
([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 0
([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => 1
([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => 1
([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => 0
([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 0
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 0
([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 0
([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => 0
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => 0
Description
The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. The correspondence between LNakayama algebras and Dyck paths is explained in [[St000684]]. A module $M$ is $n$-rigid, if $\operatorname{Ext}^i(M,M)=0$ for $1\leq i\leq n$. This statistic gives the maximal $n$ such that the minimal generator-cogenerator module $A \oplus D(A)$ of the LNakayama algebra $A$ corresponding to a Dyck path is $n$-rigid. An application is to check for maximal $n$-orthogonal objects in the module category in the sense of [2].
Matching statistic: St001195
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001195: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 50%
Values
([],3)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([],4)
 => [4,4,4,4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 0
([(2,3)],4)
 => [4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 0
([(1,2),(1,3)],4)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([(1,2),(2,3)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 0
([(1,3),(2,3)],4)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([(0,3),(1,2)],4)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 0
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 0
([(0,2),(0,3),(0,4),(4,1)],5)
 => [4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 0
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([(1,3),(1,4),(4,2)],5)
 => [15]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(0,3),(0,4),(4,1),(4,2)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 0
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2
([(0,4),(1,3),(2,3),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 0
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 0
([(0,4),(1,2),(1,3),(3,4)],5)
 => [4,4,3]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => ? = 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => [5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => ? = 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => [5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2
([(1,4),(3,2),(4,3)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(1,4),(2,3),(3,4)],5)
 => [15]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(0,3),(1,4),(4,2)],5)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(0,4),(1,2),(2,3),(2,4)],5)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 0
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 0
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,4,4,4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
 => [12,4]
 => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [14]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
 => [10,4,4]
 => [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,5,5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 2
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => [12]
 => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
 => [10,4,4]
 => [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
 => [12,4]
 => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
 => [14]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 0
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 0
([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 0
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 0
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 0
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
([(0,5),(3,2),(4,1),(5,3),(5,4)],6)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 0
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 0
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 0
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 0
([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 0
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 0
([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 0
([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 0
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 0
Description
The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$.
Matching statistic: St001526
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001526: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 50%
Values
([],3)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3 = 0 + 3
([],4)
 => [4,4,4,4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 3
([(2,3)],4)
 => [4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 3
([(1,2),(1,3)],4)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 0 + 3
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3 = 0 + 3
([(1,2),(2,3)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => 3 = 0 + 3
([(1,3),(2,3)],4)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 0 + 3
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3 = 0 + 3
([(0,3),(1,2)],4)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => 3 = 0 + 3
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 4 = 1 + 3
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 3
([(0,2),(0,3),(0,4),(4,1)],5)
 => [4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 0 + 3
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3 = 0 + 3
([(1,3),(1,4),(4,2)],5)
 => [15]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 0 + 3
([(0,3),(0,4),(4,1),(4,2)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 0 + 3
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 3
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => 3 = 0 + 3
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 4 = 1 + 3
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 3
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3 = 0 + 3
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 3
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3 = 0 + 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 3
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 1 + 3
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2 + 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 3
([(0,4),(1,3),(2,3),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 0 + 3
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2 + 3
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 3
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => ? = 1 + 3
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 4 = 1 + 3
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 3
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2 + 3
([(0,4),(1,2),(1,4),(4,3)],5)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 1 + 3
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2 + 3
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => 3 = 0 + 3
([(0,4),(1,2),(1,3),(3,4)],5)
 => [4,4,3]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => ? = 0 + 3
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 0 + 3
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 1 + 3
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2 + 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 3
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => [5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,0,1,1,0,0,1,0,0]
 => ? = 1 + 3
([(0,3),(1,2),(1,4),(3,4)],5)
 => [5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => ? = 1 + 3
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2 + 3
([(1,4),(3,2),(4,3)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 0 + 3
([(1,4),(2,3),(3,4)],5)
 => [15]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 0 + 3
([(0,3),(1,4),(4,2)],5)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 3
([(0,4),(1,2),(2,3),(2,4)],5)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 1 + 3
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => 3 = 0 + 3
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => 3 = 0 + 3
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,4,4,4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 3
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3 = 0 + 3
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
 => [12,4]
 => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 1 + 3
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [14]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2 + 3
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 3
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
 => [10,4,4]
 => [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2 + 3
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 0 + 3
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 3
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,5,5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 3
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => [12]
 => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 0 + 3
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2 + 3
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 1 + 3
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
 => [10,4,4]
 => [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2 + 3
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
 => [12,4]
 => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 1 + 3
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
 => [14]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2 + 3
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3 = 0 + 3
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3 = 0 + 3
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => 3 = 0 + 3
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3 = 0 + 3
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 4 = 1 + 3
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 4 = 1 + 3
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => 3 = 0 + 3
([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => 3 = 0 + 3
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => 3 = 0 + 3
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => 3 = 0 + 3
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 4 = 1 + 3
([(0,5),(3,2),(4,1),(5,3),(5,4)],6)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => 3 = 0 + 3
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3 = 0 + 3
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3 = 0 + 3
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3 = 0 + 3
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 4 = 1 + 3
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => 3 = 0 + 3
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => 3 = 0 + 3
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 4 = 1 + 3
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3 = 0 + 3
([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3 = 0 + 3
([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 4 = 1 + 3
([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 4 = 1 + 3
([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => 3 = 0 + 3
([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => 3 = 0 + 3
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => 3 = 0 + 3
([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => 3 = 0 + 3
([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => 3 = 0 + 3
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => 3 = 0 + 3
Description
The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path.
Matching statistic: St001488
(load all 3 compositions to match this statistic)
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001488: Skew partitions ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 50%
Values
([],3)
 => [3,3]
 => [[3,3],[]]
 => ? = 0 + 2
([],4)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => ? = 0 + 2
([(2,3)],4)
 => [4,4,4]
 => [[4,4,4],[]]
 => ? = 0 + 2
([(1,2),(1,3)],4)
 => [8]
 => [[8],[]]
 => ? = 0 + 2
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [[3,3],[]]
 => ? = 0 + 2
([(1,2),(2,3)],4)
 => [4]
 => [[4],[]]
 => 2 = 0 + 2
([(1,3),(2,3)],4)
 => [8]
 => [[8],[]]
 => ? = 0 + 2
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [[3,3],[]]
 => ? = 0 + 2
([(0,3),(1,2)],4)
 => [4,2]
 => [[4,2],[]]
 => ? = 0 + 2
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => [[3,2],[]]
 => 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => ? = 0 + 2
([(0,2),(0,3),(0,4),(4,1)],5)
 => [4,4,4]
 => [[4,4,4],[]]
 => ? = 0 + 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [8]
 => [[8],[]]
 => ? = 0 + 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [[3,3],[]]
 => ? = 0 + 2
([(1,3),(1,4),(4,2)],5)
 => [15]
 => [[15],[]]
 => ? = 0 + 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => [8]
 => [[8],[]]
 => ? = 0 + 2
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => [[5,5],[]]
 => ? = 0 + 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => [[4,2],[]]
 => ? = 0 + 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => [[3,2],[]]
 => 3 = 1 + 2
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => [[5,5],[]]
 => ? = 0 + 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => [[3,3],[]]
 => ? = 0 + 2
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => [[5,5],[]]
 => ? = 0 + 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => [[3,3],[]]
 => ? = 0 + 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => ? = 0 + 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => [[12,4],[]]
 => ? = 1 + 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => [[14],[]]
 => ? = 2 + 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [[6,6],[]]
 => ? = 2 + 2
([(0,4),(1,3),(2,3),(3,4)],5)
 => [8]
 => [[8],[]]
 => ? = 0 + 2
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => [[10,4,4],[]]
 => ? = 2 + 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4,4,4]
 => [[4,4,4],[]]
 => ? = 0 + 2
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => [[5,4],[]]
 => ? = 1 + 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => [[3,2],[]]
 => 3 = 1 + 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [[5,5,5,5],[]]
 => ? = 2 + 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [6]
 => [[6],[]]
 => ? = 2 + 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => [7]
 => [[7],[]]
 => ? = 1 + 2
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => [[10,4,4],[]]
 => ? = 2 + 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => [[4],[]]
 => 2 = 0 + 2
([(0,4),(1,2),(1,3),(3,4)],5)
 => [4,4,3]
 => [[4,4,3],[]]
 => ? = 0 + 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [8]
 => [[8],[]]
 => ? = 0 + 2
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => [[12,4],[]]
 => ? = 1 + 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => [[14],[]]
 => ? = 2 + 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [[6,6],[]]
 => ? = 2 + 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => [5,3]
 => [[5,3],[]]
 => ? = 1 + 2
([(0,3),(1,2),(1,4),(3,4)],5)
 => [5,4]
 => [[5,4],[]]
 => ? = 1 + 2
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => [6]
 => [[6],[]]
 => ? = 2 + 2
([(1,4),(3,2),(4,3)],5)
 => [5]
 => [[5],[]]
 => 2 = 0 + 2
([(1,4),(2,3),(3,4)],5)
 => [15]
 => [[15],[]]
 => ? = 0 + 2
([(0,3),(1,4),(4,2)],5)
 => [5,5]
 => [[5,5],[]]
 => ? = 0 + 2
([(0,4),(1,2),(2,3),(2,4)],5)
 => [7]
 => [[7],[]]
 => ? = 1 + 2
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,2]
 => [[4,2],[]]
 => ? = 0 + 2
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => [[4],[]]
 => 2 = 0 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => ? = 0 + 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [[3,3],[]]
 => ? = 0 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
 => [12,4]
 => [[12,4],[]]
 => ? = 1 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [14]
 => [[14],[]]
 => ? = 2 + 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,6]
 => [[6,6],[]]
 => ? = 2 + 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
 => [10,4,4]
 => [[10,4,4],[]]
 => ? = 2 + 2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [3,2]
 => [[3,2],[]]
 => 3 = 1 + 2
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [3,2]
 => [[3,2],[]]
 => 3 = 1 + 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => [4]
 => [[4],[]]
 => 2 = 0 + 2
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => [5]
 => [[5],[]]
 => 2 = 0 + 2
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
 => [4]
 => [[4],[]]
 => 2 = 0 + 2
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => [4]
 => [[4],[]]
 => 2 = 0 + 2
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [3,2]
 => [[3,2],[]]
 => 3 = 1 + 2
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => [5]
 => [[5],[]]
 => 2 = 0 + 2
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => [5]
 => [[5],[]]
 => 2 = 0 + 2
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => [3,2]
 => [[3,2],[]]
 => 3 = 1 + 2
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
 => [4]
 => [[4],[]]
 => 2 = 0 + 2
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => [3,2]
 => [[3,2],[]]
 => 3 = 1 + 2
([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)
 => [3,2]
 => [[3,2],[]]
 => 3 = 1 + 2
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => [5]
 => [[5],[]]
 => 2 = 0 + 2
([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7)
 => [3,2]
 => [[3,2],[]]
 => 3 = 1 + 2
([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)
 => [4]
 => [[4],[]]
 => 2 = 0 + 2
([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)
 => [5]
 => [[5],[]]
 => 2 = 0 + 2
([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
 => [4]
 => [[4],[]]
 => 2 = 0 + 2
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => [4]
 => [[4],[]]
 => 2 = 0 + 2
Description
The number of corners of a skew partition. This is also known as the number of removable cells of the skew partition.
Matching statistic: St001435
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00189: Skew partitions —rotate⟶ Skew partitions
St001435: Skew partitions ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 50%
Values
([],3)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0
([],4)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => [[4,4,4,4,4,4],[]]
 => ? = 0
([(2,3)],4)
 => [4,4,4]
 => [[4,4,4],[]]
 => [[4,4,4],[]]
 => ? = 0
([(1,2),(1,3)],4)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0
([(1,2),(2,3)],4)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(1,3),(2,3)],4)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0
([(0,3),(1,2)],4)
 => [4,2]
 => [[4,2],[]]
 => [[4,4],[2]]
 => ? = 0
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => [[4,4,4,4,4,4],[]]
 => ? = 0
([(0,2),(0,3),(0,4),(4,1)],5)
 => [4,4,4]
 => [[4,4,4],[]]
 => [[4,4,4],[]]
 => ? = 0
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0
([(1,3),(1,4),(4,2)],5)
 => [15]
 => [[15],[]]
 => [[15],[]]
 => ? = 0
([(0,3),(0,4),(4,1),(4,2)],5)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => [[5,5],[]]
 => [[5,5],[]]
 => ? = 0
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => [[4,2],[]]
 => [[4,4],[2]]
 => ? = 0
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => [[5,5],[]]
 => [[5,5],[]]
 => ? = 0
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => [[5,5],[]]
 => [[5,5],[]]
 => ? = 0
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => [[4,4,4,4,4,4],[]]
 => ? = 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => [[12,4],[]]
 => [[12,12],[8]]
 => ? = 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => [[14],[]]
 => [[14],[]]
 => ? = 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [[6,6],[]]
 => [[6,6],[]]
 => ? = 2
([(0,4),(1,3),(2,3),(3,4)],5)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => [[10,4,4],[]]
 => [[10,10,10],[6,6]]
 => ? = 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4,4,4]
 => [[4,4,4],[]]
 => [[4,4,4],[]]
 => ? = 0
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => [[5,4],[]]
 => [[5,5],[1]]
 => ? = 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [[5,5,5,5],[]]
 => [[5,5,5,5],[]]
 => ? = 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [6]
 => [[6],[]]
 => [[6],[]]
 => ? = 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => [7]
 => [[7],[]]
 => [[7],[]]
 => ? = 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => [[10,4,4],[]]
 => [[10,10,10],[6,6]]
 => ? = 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(0,4),(1,2),(1,3),(3,4)],5)
 => [4,4,3]
 => [[4,4,3],[]]
 => [[4,4,4],[1]]
 => ? = 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => [[12,4],[]]
 => [[12,12],[8]]
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => [[14],[]]
 => [[14],[]]
 => ? = 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [[6,6],[]]
 => [[6,6],[]]
 => ? = 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => [5,3]
 => [[5,3],[]]
 => [[5,5],[2]]
 => ? = 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => [5,4]
 => [[5,4],[]]
 => [[5,5],[1]]
 => ? = 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => [6]
 => [[6],[]]
 => [[6],[]]
 => ? = 2
([(1,4),(3,2),(4,3)],5)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 0
([(1,4),(2,3),(3,4)],5)
 => [15]
 => [[15],[]]
 => [[15],[]]
 => ? = 0
([(0,3),(1,4),(4,2)],5)
 => [5,5]
 => [[5,5],[]]
 => [[5,5],[]]
 => ? = 0
([(0,4),(1,2),(2,3),(2,4)],5)
 => [7]
 => [[7],[]]
 => [[7],[]]
 => ? = 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,2]
 => [[4,2],[]]
 => [[4,4],[2]]
 => ? = 0
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => [[4,4,4,4,4,4],[]]
 => ? = 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
 => [12,4]
 => [[12,4],[]]
 => [[12,12],[8]]
 => ? = 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [14]
 => [[14],[]]
 => [[14],[]]
 => ? = 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,6]
 => [[6,6],[]]
 => [[6,6],[]]
 => ? = 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
 => [10,4,4]
 => [[10,4,4],[]]
 => [[10,10,10],[6,6]]
 => ? = 2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 0
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 0
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 0
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 0
([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 0
([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
Description
The number of missing boxes in the first row.
Matching statistic: St001438
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00189: Skew partitions —rotate⟶ Skew partitions
St001438: Skew partitions ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 50%
Values
([],3)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0
([],4)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => [[4,4,4,4,4,4],[]]
 => ? = 0
([(2,3)],4)
 => [4,4,4]
 => [[4,4,4],[]]
 => [[4,4,4],[]]
 => ? = 0
([(1,2),(1,3)],4)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0
([(1,2),(2,3)],4)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(1,3),(2,3)],4)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0
([(0,3),(1,2)],4)
 => [4,2]
 => [[4,2],[]]
 => [[4,4],[2]]
 => ? = 0
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => [[4,4,4,4,4,4],[]]
 => ? = 0
([(0,2),(0,3),(0,4),(4,1)],5)
 => [4,4,4]
 => [[4,4,4],[]]
 => [[4,4,4],[]]
 => ? = 0
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0
([(1,3),(1,4),(4,2)],5)
 => [15]
 => [[15],[]]
 => [[15],[]]
 => ? = 0
([(0,3),(0,4),(4,1),(4,2)],5)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => [[5,5],[]]
 => [[5,5],[]]
 => ? = 0
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => [[4,2],[]]
 => [[4,4],[2]]
 => ? = 0
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => [[5,5],[]]
 => [[5,5],[]]
 => ? = 0
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => [[5,5],[]]
 => [[5,5],[]]
 => ? = 0
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => [[4,4,4,4,4,4],[]]
 => ? = 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => [[12,4],[]]
 => [[12,12],[8]]
 => ? = 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => [[14],[]]
 => [[14],[]]
 => ? = 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [[6,6],[]]
 => [[6,6],[]]
 => ? = 2
([(0,4),(1,3),(2,3),(3,4)],5)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => [[10,4,4],[]]
 => [[10,10,10],[6,6]]
 => ? = 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4,4,4]
 => [[4,4,4],[]]
 => [[4,4,4],[]]
 => ? = 0
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => [[5,4],[]]
 => [[5,5],[1]]
 => ? = 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [[5,5,5,5],[]]
 => [[5,5,5,5],[]]
 => ? = 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [6]
 => [[6],[]]
 => [[6],[]]
 => ? = 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => [7]
 => [[7],[]]
 => [[7],[]]
 => ? = 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => [[10,4,4],[]]
 => [[10,10,10],[6,6]]
 => ? = 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(0,4),(1,2),(1,3),(3,4)],5)
 => [4,4,3]
 => [[4,4,3],[]]
 => [[4,4,4],[1]]
 => ? = 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => [[12,4],[]]
 => [[12,12],[8]]
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => [[14],[]]
 => [[14],[]]
 => ? = 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [[6,6],[]]
 => [[6,6],[]]
 => ? = 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => [5,3]
 => [[5,3],[]]
 => [[5,5],[2]]
 => ? = 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => [5,4]
 => [[5,4],[]]
 => [[5,5],[1]]
 => ? = 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => [6]
 => [[6],[]]
 => [[6],[]]
 => ? = 2
([(1,4),(3,2),(4,3)],5)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 0
([(1,4),(2,3),(3,4)],5)
 => [15]
 => [[15],[]]
 => [[15],[]]
 => ? = 0
([(0,3),(1,4),(4,2)],5)
 => [5,5]
 => [[5,5],[]]
 => [[5,5],[]]
 => ? = 0
([(0,4),(1,2),(2,3),(2,4)],5)
 => [7]
 => [[7],[]]
 => [[7],[]]
 => ? = 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,2]
 => [[4,2],[]]
 => [[4,4],[2]]
 => ? = 0
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => [[4,4,4,4,4,4],[]]
 => ? = 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
 => [12,4]
 => [[12,4],[]]
 => [[12,12],[8]]
 => ? = 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [14]
 => [[14],[]]
 => [[14],[]]
 => ? = 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,6]
 => [[6,6],[]]
 => [[6,6],[]]
 => ? = 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
 => [10,4,4]
 => [[10,4,4],[]]
 => [[10,10,10],[6,6]]
 => ? = 2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 0
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 0
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 0
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 0
([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 1
([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 0
([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 0
Description
The number of missing boxes of a skew partition.
Matching statistic: St001487
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00189: Skew partitions —rotate⟶ Skew partitions
St001487: Skew partitions ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 50%
Values
([],3)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0 + 1
([],4)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => [[4,4,4,4,4,4],[]]
 => ? = 0 + 1
([(2,3)],4)
 => [4,4,4]
 => [[4,4,4],[]]
 => [[4,4,4],[]]
 => ? = 0 + 1
([(1,2),(1,3)],4)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0 + 1
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0 + 1
([(1,2),(2,3)],4)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 1 = 0 + 1
([(1,3),(2,3)],4)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0 + 1
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0 + 1
([(0,3),(1,2)],4)
 => [4,2]
 => [[4,2],[]]
 => [[4,4],[2]]
 => ? = 0 + 1
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 2 = 1 + 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => [[4,4,4,4,4,4],[]]
 => ? = 0 + 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => [4,4,4]
 => [[4,4,4],[]]
 => [[4,4,4],[]]
 => ? = 0 + 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0 + 1
([(1,3),(1,4),(4,2)],5)
 => [15]
 => [[15],[]]
 => [[15],[]]
 => ? = 0 + 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0 + 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => [[5,5],[]]
 => [[5,5],[]]
 => ? = 0 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => [[4,2],[]]
 => [[4,4],[2]]
 => ? = 0 + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 2 = 1 + 1
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => [[5,5],[]]
 => [[5,5],[]]
 => ? = 0 + 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0 + 1
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => [[5,5],[]]
 => [[5,5],[]]
 => ? = 0 + 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => [[4,4,4,4,4,4],[]]
 => ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => [[12,4],[]]
 => [[12,12],[8]]
 => ? = 1 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => [[14],[]]
 => [[14],[]]
 => ? = 2 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [[6,6],[]]
 => [[6,6],[]]
 => ? = 2 + 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => [[10,4,4],[]]
 => [[10,10,10],[6,6]]
 => ? = 2 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4,4,4]
 => [[4,4,4],[]]
 => [[4,4,4],[]]
 => ? = 0 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => [[5,4],[]]
 => [[5,5],[1]]
 => ? = 1 + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 2 = 1 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [[5,5,5,5],[]]
 => [[5,5,5,5],[]]
 => ? = 2 + 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [6]
 => [[6],[]]
 => [[6],[]]
 => ? = 2 + 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => [7]
 => [[7],[]]
 => [[7],[]]
 => ? = 1 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => [[10,4,4],[]]
 => [[10,10,10],[6,6]]
 => ? = 2 + 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 1 = 0 + 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => [4,4,3]
 => [[4,4,3],[]]
 => [[4,4,4],[1]]
 => ? = 0 + 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [8]
 => [[8],[]]
 => [[8],[]]
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => [[12,4],[]]
 => [[12,12],[8]]
 => ? = 1 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => [[14],[]]
 => [[14],[]]
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [[6,6],[]]
 => [[6,6],[]]
 => ? = 2 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => [5,3]
 => [[5,3],[]]
 => [[5,5],[2]]
 => ? = 1 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => [5,4]
 => [[5,4],[]]
 => [[5,5],[1]]
 => ? = 1 + 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => [6]
 => [[6],[]]
 => [[6],[]]
 => ? = 2 + 1
([(1,4),(3,2),(4,3)],5)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
 => [15]
 => [[15],[]]
 => [[15],[]]
 => ? = 0 + 1
([(0,3),(1,4),(4,2)],5)
 => [5,5]
 => [[5,5],[]]
 => [[5,5],[]]
 => ? = 0 + 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => [7]
 => [[7],[]]
 => [[7],[]]
 => ? = 1 + 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,2]
 => [[4,2],[]]
 => [[4,4],[2]]
 => ? = 0 + 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 1 = 0 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => [[4,4,4,4,4,4],[]]
 => ? = 0 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [[3,3],[]]
 => [[3,3],[]]
 => ? = 0 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
 => [12,4]
 => [[12,4],[]]
 => [[12,12],[8]]
 => ? = 1 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [14]
 => [[14],[]]
 => [[14],[]]
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,6]
 => [[6,6],[]]
 => [[6,6],[]]
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
 => [10,4,4]
 => [[10,4,4],[]]
 => [[10,10,10],[6,6]]
 => ? = 2 + 1
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 2 = 1 + 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 2 = 1 + 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 1 = 0 + 1
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 1 = 0 + 1
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 1 = 0 + 1
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 1 = 0 + 1
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 2 = 1 + 1
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 1 = 0 + 1
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 1 = 0 + 1
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 2 = 1 + 1
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 1 = 0 + 1
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 2 = 1 + 1
([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 2 = 1 + 1
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 1 = 0 + 1
([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7)
 => [3,2]
 => [[3,2],[]]
 => [[3,3],[1]]
 => 2 = 1 + 1
([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 1 = 0 + 1
([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)
 => [5]
 => [[5],[]]
 => [[5],[]]
 => 1 = 0 + 1
([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 1 = 0 + 1
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => [4]
 => [[4],[]]
 => [[4],[]]
 => 1 = 0 + 1
Description
The number of inner corners of a skew partition.