Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001232
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [1]
 => [1,0,1,0]
 => [1,0,1,0]
 => 1
([],2)
 => [1,1]
 => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => 2
([(0,1)],2)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 1
([],3)
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 3
([(0,2),(2,1)],3)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
([],4)
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4
([(0,2),(0,3),(3,1)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,1),(0,2),(1,3),(2,3)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,2),(2,3)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,3),(3,1),(3,2)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,3),(1,2)],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
([(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
([(0,3),(2,1),(3,2)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
([(0,3),(1,2),(2,3)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([],5)
 => [1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 5
([(0,2),(0,3),(0,4),(4,1)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,3),(1,4),(4,2)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,3),(0,4),(4,1),(4,2)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,2),(1,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(2,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,4),(4,2),(4,3)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,4),(2,4),(4,3)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,4),(1,4),(2,3),(4,2)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,4),(1,3),(2,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,4),(1,4),(2,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,4),(1,2),(1,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,4),(3,2),(4,3)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,3),(3,4),(4,1),(4,2)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(1,4),(2,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,4),(1,2),(2,4),(4,3)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,4),(3,2),(4,1),(4,3)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,4),(2,3),(3,1),(4,2)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([],6)
 => [1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => 6
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(1,3),(1,4),(1,5),(5,2)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001227
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
St001227: Dyck paths ⟶ ℤResult quality: 83% ●values known / values provided: 94%●distinct values known / distinct values provided: 83%
Values
([],1)
 => [1]
 => [1,0,1,0]
 => [1,0,1,0]
 => 1
([],2)
 => [1,1]
 => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => 2
([(0,1)],2)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 1
([],3)
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 3
([(0,2),(2,1)],3)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
([],4)
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4
([(0,2),(0,3),(3,1)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,1),(0,2),(1,3),(2,3)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,2),(2,3)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,3),(3,1),(3,2)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,3),(1,2)],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
([(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
([(0,3),(2,1),(3,2)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
([(0,3),(1,2),(2,3)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([],5)
 => [1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 5
([(0,2),(0,3),(0,4),(4,1)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,3),(1,4),(4,2)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,3),(0,4),(4,1),(4,2)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,2),(1,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(2,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,4),(4,2),(4,3)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,4),(2,4),(4,3)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,4),(1,4),(2,3),(4,2)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,4),(1,3),(2,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,4),(1,4),(2,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,4),(1,2),(1,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,4),(3,2),(4,3)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,3),(3,4),(4,1),(4,2)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(1,4),(2,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,4),(1,2),(2,4),(4,3)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,4),(3,2),(4,1),(4,3)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,4),(2,3),(3,1),(4,2)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([],6)
 => [1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 6
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(1,3),(1,4),(1,5),(5,2)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 1
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => [6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => [6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => [6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => [6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => [6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => [6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => [6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4
([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => [6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4
([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => [6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4
([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => [6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4
([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => [6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4
([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => [6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
 => [5,3,2,2,2]
 => [1,1,0,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
 => ? = 5
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
 => [5,3,2,2,2]
 => [1,1,0,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
 => ? = 5
([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
 => [6,4]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
 => [6,4,2]
 => [1,1,1,1,0,0,1,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => [6,3,1]
 => [1,1,1,1,0,1,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4
([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
 => [6,4,1]
 => [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
([(0,6),(0,7),(1,9),(2,8),(3,5),(4,2),(5,1),(5,8),(6,3),(7,4),(8,9)],10)
 => [6,4]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
([(0,5),(1,6),(2,9),(3,6),(3,9),(4,7),(5,1),(5,2),(5,3),(6,8),(8,7),(9,4),(9,8)],10)
 => [6,3,1]
 => [1,1,1,1,0,1,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4
([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
 => [6,4]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
 => [6,4]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11)
 => [6,4,1]
 => [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
([(0,3),(0,4),(1,11),(2,10),(3,2),(3,9),(4,1),(4,9),(5,7),(5,8),(6,12),(7,12),(8,12),(9,5),(9,10),(9,11),(10,6),(10,7),(11,6),(11,8)],13)
 => [6,4,3]
 => [1,1,1,1,0,0,0,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
 => [6,3,2]
 => [1,1,1,1,0,0,1,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
 => [6,4]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
 => [6,4]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3
Description
The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra.
Matching statistic: St001265
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
St001265: Dyck paths ⟶ ℤResult quality: 83% ●values known / values provided: 94%●distinct values known / distinct values provided: 83%
Values
([],1)
 => [1]
 => [1,0,1,0]
 => [1,0,1,0]
 => 0 = 1 - 1
([],2)
 => [1,1]
 => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => 1 = 2 - 1
([(0,1)],2)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 0 = 1 - 1
([],3)
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 2 = 3 - 1
([(0,2),(2,1)],3)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 0 = 1 - 1
([],4)
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 3 = 4 - 1
([(0,2),(0,3),(3,1)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(1,2),(2,3)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(0,3),(3,1),(3,2)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(0,3),(1,2)],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 1 = 2 - 1
([(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 1 = 2 - 1
([(0,3),(2,1),(3,2)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 0 = 1 - 1
([(0,3),(1,2),(2,3)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([],5)
 => [1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 4 = 5 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(1,3),(1,4),(4,2)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 3 = 4 - 1
([(2,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(1,4),(4,2),(4,3)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(1,4),(2,4),(4,3)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 3 = 4 - 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 3 = 4 - 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 3 = 4 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(1,4),(3,2),(4,3)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 3 = 4 - 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 3 = 4 - 1
([(1,4),(2,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2 = 3 - 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 3 = 4 - 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 3 = 4 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 0 = 1 - 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 3 = 4 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 3 = 4 - 1
([],6)
 => [1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 6 - 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 3 = 4 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 3 = 4 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 3 = 4 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 3 = 4 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 3 = 4 - 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 3 = 4 - 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 6 - 1
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => [6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5 - 1
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => [6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5 - 1
([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => [6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5 - 1
([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => [6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5 - 1
([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => [6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5 - 1
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => [6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5 - 1
([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => [6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4 - 1
([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => [6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4 - 1
([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => [6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4 - 1
([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => [6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4 - 1
([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => [6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4 - 1
([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => [6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
 => [5,3,2,2,2]
 => [1,1,0,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
 => ? = 5 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
 => [5,3,2,2,2]
 => [1,1,0,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
 => ? = 5 - 1
([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
 => [6,4]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3 - 1
([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
 => [6,4,2]
 => [1,1,1,1,0,0,1,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3 - 1
([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => [6,3,1]
 => [1,1,1,1,0,1,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4 - 1
([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
 => [6,4,1]
 => [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3 - 1
([(0,6),(0,7),(1,9),(2,8),(3,5),(4,2),(5,1),(5,8),(6,3),(7,4),(8,9)],10)
 => [6,4]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3 - 1
([(0,5),(1,6),(2,9),(3,6),(3,9),(4,7),(5,1),(5,2),(5,3),(6,8),(8,7),(9,4),(9,8)],10)
 => [6,3,1]
 => [1,1,1,1,0,1,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4 - 1
([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
 => [6,4]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3 - 1
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
 => [6,4]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3 - 1
([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11)
 => [6,4,1]
 => [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3 - 1
([(0,3),(0,4),(1,11),(2,10),(3,2),(3,9),(4,1),(4,9),(5,7),(5,8),(6,12),(7,12),(8,12),(9,5),(9,10),(9,11),(10,6),(10,7),(11,6),(11,8)],13)
 => [6,4,3]
 => [1,1,1,1,0,0,0,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3 - 1
([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
 => [6,3,2]
 => [1,1,1,1,0,0,1,0,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4 - 1
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
 => [6,4]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3 - 1
([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
 => [6,4]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 3 - 1
Description
The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra.
Matching statistic: St001000
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
St001000: Dyck paths ⟶ ℤResult quality: 67% ●values known / values provided: 78%●distinct values known / distinct values provided: 67%
Values
([],1)
 => [1]
 => [1,0,1,0]
 => [1,0,1,0]
 => 1
([],2)
 => [1,1]
 => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => 2
([(0,1)],2)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 1
([],3)
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 3
([(0,2),(2,1)],3)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
([],4)
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4
([(0,2),(0,3),(3,1)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,1),(0,2),(1,3),(2,3)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,2),(2,3)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,3),(3,1),(3,2)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,3),(1,2)],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
([(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
([(0,3),(2,1),(3,2)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
([(0,3),(1,2),(2,3)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([],5)
 => [1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => ? = 5
([(0,2),(0,3),(0,4),(4,1)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,3),(1,4),(4,2)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,3),(0,4),(4,1),(4,2)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,2),(1,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(2,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,4),(4,2),(4,3)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,4),(2,4),(4,3)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,4),(1,4),(2,3),(4,2)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,4),(1,3),(2,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,4),(1,4),(2,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,4),(1,2),(1,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(1,4),(3,2),(4,3)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,3),(3,4),(4,1),(4,2)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(1,4),(2,3),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
([(0,4),(1,2),(2,4),(4,3)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,4),(3,2),(4,1),(4,3)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,4),(2,3),(3,1),(4,2)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
([],6)
 => [1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 6
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(1,3),(1,4),(1,5),(5,2)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(1,5),(3,4),(4,2),(5,3)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 1
([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(1,3),(1,4),(1,5),(1,6),(6,2)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(2,4),(2,5),(2,6),(6,3)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(1,4),(1,5),(1,6),(6,2),(6,3)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(2,3),(2,4),(2,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(3,4),(3,5),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(2,5),(2,6),(6,3),(6,4)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(1,5),(1,6),(6,2),(6,3),(6,4)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(3,4),(3,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 4
([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5
([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 4
([(4,5),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(3,4),(4,5),(4,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(2,6),(6,3),(6,4),(6,5)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(1,6),(6,2),(6,3),(6,4),(6,5)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(3,6),(4,6),(6,5)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
([(2,6),(3,6),(4,6),(6,5)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 5
Description
Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path.