Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001902
(load all 4 compositions to match this statistic)
Mapping
St001902: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 0
([],2)
 => 2
([(0,1)],2)
 => 0
([],3)
 => 6
([(1,2)],3)
 => 2
([(0,1),(0,2)],3)
 => 2
([(0,2),(2,1)],3)
 => 0
([(0,2),(1,2)],3)
 => 2
([],4)
 => 12
([(2,3)],4)
 => 6
([(1,2),(1,3)],4)
 => 5
([(0,1),(0,2),(0,3)],4)
 => 6
([(0,2),(0,3),(3,1)],4)
 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,2),(2,3)],4)
 => 2
([(0,3),(3,1),(3,2)],4)
 => 2
([(1,3),(2,3)],4)
 => 5
([(0,3),(1,3),(3,2)],4)
 => 2
([(0,3),(1,3),(2,3)],4)
 => 6
([(0,3),(1,2)],4)
 => 2
([(0,3),(1,2),(1,3)],4)
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
([(0,3),(2,1),(3,2)],4)
 => 0
([(0,3),(1,2),(2,3)],4)
 => 2
([],5)
 => 20
([(3,4)],5)
 => 12
([(2,3),(2,4)],5)
 => 10
([(1,2),(1,3),(1,4)],5)
 => 10
([(0,1),(0,2),(0,3),(0,4)],5)
 => 12
([(0,2),(0,3),(0,4),(4,1)],5)
 => 6
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 5
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 6
([(1,3),(1,4),(4,2)],5)
 => 5
([(0,3),(0,4),(4,1),(4,2)],5)
 => 5
([(1,2),(1,3),(2,4),(3,4)],5)
 => 4
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
([(0,3),(0,4),(3,2),(4,1)],5)
 => 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 3
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 4
([(2,3),(3,4)],5)
 => 6
([(1,4),(4,2),(4,3)],5)
 => 5
([(0,4),(4,1),(4,2),(4,3)],5)
 => 6
([(2,4),(3,4)],5)
 => 10
([(1,4),(2,4),(4,3)],5)
 => 5
([(0,4),(1,4),(4,2),(4,3)],5)
 => 4
([(1,4),(2,4),(3,4)],5)
 => 10
([(0,4),(1,4),(2,4),(4,3)],5)
 => 6
([(0,4),(1,4),(2,4),(3,4)],5)
 => 12
([(0,4),(1,4),(2,3)],5)
 => 5
([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
Description
The number of potential covers of a poset. A potential cover is a pair of uncomparable elements $(x, y)$ which can be added to the poset without adding any other relations. For example, let $P$ be the disjoint union of a single relation $(1, 2)$ with the one element poset $0$. Then the relation $(0, 1)$ cannot be added without adding also $(0, 2)$, however, the relations $(0, 2)$ and $(1, 0)$ are potential covers.
Matching statistic: St001232
(load all 2 compositions to match this statistic)
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 12%
Values
([],1)
 => [1]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0
([],2)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
([(0,1)],2)
 => [1]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0
([],3)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? = 6
([(1,2)],3)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => ? = 2
([(0,1),(0,2)],3)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
([(0,2),(2,1)],3)
 => [1]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0
([(0,2),(1,2)],3)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
([],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]
 => ? = 12
([(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]
 => ? = 6
([(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]
 => ? = 5
([(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]
 => ? = 6
([(0,2),(0,3),(3,1)],4)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => ? = 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
([(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]
 => ? = 2
([(0,3),(3,1),(3,2)],4)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
([(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]
 => ? = 5
([(0,3),(1,3),(3,2)],4)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
([(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]
 => ? = 6
([(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]
 => ? = 2
([(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]
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 4
([(0,3),(2,1),(3,2)],4)
 => [1]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0
([(0,3),(1,2),(2,3)],4)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => ? = 2
([],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 20
([(3,4)],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 12
([(2,3),(2,4)],5)
 => [10,10,10,10]
 => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 10
([(1,2),(1,3),(1,4)],5)
 => [15,15]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 10
([(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]
 => ? = 12
([(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]
 => ? = 6
([(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]
 => ? = 5
([(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]
 => ? = 6
([(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]
 => ? = 5
([(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]
 => ? = 5
([(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]
 => ? = 4
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
([(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]
 => ? = 2
([(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]
 => 3
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 4
([(2,3),(3,4)],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]
 => ? = 6
([(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]
 => ? = 5
([(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]
 => ? = 6
([(2,4),(3,4)],5)
 => [10,10,10,10]
 => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 10
([(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]
 => ? = 5
([(0,4),(1,4),(4,2),(4,3)],5)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 4
([(1,4),(2,4),(3,4)],5)
 => [15,15]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 10
([(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]
 => ? = 6
([(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]
 => ? = 12
([(0,4),(1,4),(2,3)],5)
 => [10,10]
 => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 5
([(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]
 => ? = 4
([(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]
 => ? = 6
([(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]
 => ? = 8
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 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]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 5
([(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]
 => ? = 7
([(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]
 => ? = 6
([(1,4),(2,3)],5)
 => [5,5,5,5,5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 6
([(1,4),(2,3),(2,4)],5)
 => [15,5,5]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 7
([(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]
 => ? = 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]
 => 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]
 => ? = 8
([(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]
 => ? = 4
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 4
([(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]
 => ? = 3
([(0,4),(1,2),(1,3)],5)
 => [10,10]
 => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 5
([(0,3),(3,4),(4,1),(4,2)],5)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [1]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
([(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]
 => 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]
 => 3
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
([(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]
 => 3
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => [1]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.