searching the database
Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St001876
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001876: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00065: Permutations —permutation poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001876: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1},{2},{3}}
=> [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,3,4}}
=> [2,3,4,1] => ([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> 0
{{1,3},{2,4}}
=> [3,4,1,2] => ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
{{1},{2},{3},{4}}
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
{{1,2,3,4,5}}
=> [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => ([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> 0
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => ([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 0
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
{{1},{2,3,4,5}}
=> [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,2),(2,1)],3)
=> 0
{{1,4},{2,5},{3}}
=> [4,5,3,1,2] => ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
{{1},{2,4},{3,5}}
=> [1,4,5,2,3] => ([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
{{1,5},{2},{3},{4}}
=> [5,2,3,4,1] => ([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 0
{{1},{2},{3},{4},{5}}
=> [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
{{1,2,3,4,5,6}}
=> [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
{{1,2,3,4,5},{6}}
=> [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
{{1,2,3,4},{5,6}}
=> [2,3,4,1,6,5] => ([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
{{1,2,3,4},{5},{6}}
=> [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,3,5},{4,6}}
=> [2,3,5,6,1,4] => ([(0,5),(1,4),(3,2),(4,3),(4,5)],6)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 1
{{1,2,3},{4,5,6}}
=> [2,3,1,5,6,4] => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
{{1,2,3},{4,5},{6}}
=> [2,3,1,5,4,6] => ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,3},{4},{5,6}}
=> [2,3,1,4,6,5] => ([(0,5),(1,2),(2,5),(5,3),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,4,6},{3,5}}
=> [2,4,5,6,3,1] => ([(1,3),(1,5),(4,2),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,4},{3,5,6}}
=> [2,4,5,1,6,3] => ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 1
{{1,2,4},{3,5},{6}}
=> [2,4,5,1,3,6] => ([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
{{1,2},{3,4,5,6}}
=> [2,1,4,5,6,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
{{1,2},{3,4,5},{6}}
=> [2,1,4,5,3,6] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2},{3,4},{5,6}}
=> [2,1,4,3,6,5] => ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,5},{3,6},{4}}
=> [2,5,6,4,1,3] => ([(0,5),(1,3),(1,4),(1,5),(4,2)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
{{1,2},{3,5},{4,6}}
=> [2,1,5,6,3,4] => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
{{1,2},{3},{4,5,6}}
=> [2,1,3,5,6,4] => ([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,6},{3},{4},{5}}
=> [2,6,3,4,5,1] => ([(1,3),(1,5),(4,2),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,3,4,5},{2,6}}
=> [3,6,4,5,1,2] => ([(0,4),(1,3),(1,5),(5,2)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
{{1,3,4},{2,6},{5}}
=> [3,6,4,1,5,2] => ([(0,4),(0,5),(1,2),(1,3),(3,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,3,5,6},{2,4}}
=> [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,3,5},{2,4,6}}
=> [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 3
{{1,3,5},{2,4},{6}}
=> [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,3},{2,4,5,6}}
=> [3,4,1,5,6,2] => ([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
=> ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 1
{{1,3},{2,4,5},{6}}
=> [3,4,1,5,2,6] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
{{1,3,6},{2,4},{5}}
=> [3,4,6,2,5,1] => ([(1,5),(2,3),(3,4),(3,5)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
{{1,3},{2,4},{5,6}}
=> [3,4,1,2,6,5] => ([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
{{1,3},{2,4},{5},{6}}
=> [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
{{1,3},{2,5},{4,6}}
=> [3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> 2
{{1,3,6},{2},{4},{5}}
=> [3,2,6,4,5,1] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,4,5},{2,3,6}}
=> [4,3,6,5,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,3)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
{{1,4},{2,3,6},{5}}
=> [4,3,6,1,5,2] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,5},{2,3,4,6}}
=> [5,3,4,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
Description
The number of 2-regular simple modules in the incidence algebra of the lattice.
Matching statistic: St001877
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001877: Lattices ⟶ ℤResult quality: 60% ●values known / values provided: 89%●distinct values known / distinct values provided: 60%
Mp00065: Permutations —permutation poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001877: Lattices ⟶ ℤResult quality: 60% ●values known / values provided: 89%●distinct values known / distinct values provided: 60%
Values
{{1},{2},{3}}
=> [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,3,4}}
=> [2,3,4,1] => ([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> 0
{{1,3},{2,4}}
=> [3,4,1,2] => ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
{{1},{2},{3},{4}}
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
{{1,2,3,4,5}}
=> [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => ([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> 0
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => ([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 0
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
{{1},{2,3,4,5}}
=> [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,2),(2,1)],3)
=> 0
{{1,4},{2,5},{3}}
=> [4,5,3,1,2] => ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
{{1},{2,4},{3,5}}
=> [1,4,5,2,3] => ([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
{{1,5},{2},{3},{4}}
=> [5,2,3,4,1] => ([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 0
{{1},{2},{3},{4},{5}}
=> [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
{{1,2,3,4,5,6}}
=> [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
{{1,2,3,4,5},{6}}
=> [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
{{1,2,3,4},{5,6}}
=> [2,3,4,1,6,5] => ([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
{{1,2,3,4},{5},{6}}
=> [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,3,5},{4,6}}
=> [2,3,5,6,1,4] => ([(0,5),(1,4),(3,2),(4,3),(4,5)],6)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 1
{{1,2,3},{4,5,6}}
=> [2,3,1,5,6,4] => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
{{1,2,3},{4,5},{6}}
=> [2,3,1,5,4,6] => ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,3},{4},{5,6}}
=> [2,3,1,4,6,5] => ([(0,5),(1,2),(2,5),(5,3),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,4,6},{3,5}}
=> [2,4,5,6,3,1] => ([(1,3),(1,5),(4,2),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,4},{3,5,6}}
=> [2,4,5,1,6,3] => ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 1
{{1,2,4},{3,5},{6}}
=> [2,4,5,1,3,6] => ([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
{{1,2},{3,4,5,6}}
=> [2,1,4,5,6,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
{{1,2},{3,4,5},{6}}
=> [2,1,4,5,3,6] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2},{3,4},{5,6}}
=> [2,1,4,3,6,5] => ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,5},{3,6},{4}}
=> [2,5,6,4,1,3] => ([(0,5),(1,3),(1,4),(1,5),(4,2)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
{{1,2},{3,5},{4,6}}
=> [2,1,5,6,3,4] => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
{{1,2},{3},{4,5,6}}
=> [2,1,3,5,6,4] => ([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,2,6},{3},{4},{5}}
=> [2,6,3,4,5,1] => ([(1,3),(1,5),(4,2),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,3,4,5},{2,6}}
=> [3,6,4,5,1,2] => ([(0,4),(1,3),(1,5),(5,2)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
{{1,3,4},{2,6},{5}}
=> [3,6,4,1,5,2] => ([(0,4),(0,5),(1,2),(1,3),(3,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,3,5,6},{2,4}}
=> [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,3,5},{2,4,6}}
=> [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3
{{1,3,5},{2,4},{6}}
=> [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,3},{2,4,5,6}}
=> [3,4,1,5,6,2] => ([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
=> ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 1
{{1,3},{2,4,5},{6}}
=> [3,4,1,5,2,6] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
{{1,3,6},{2,4},{5}}
=> [3,4,6,2,5,1] => ([(1,5),(2,3),(3,4),(3,5)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
{{1,3},{2,4},{5,6}}
=> [3,4,1,2,6,5] => ([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
{{1,3},{2,4},{5},{6}}
=> [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
{{1,3},{2,5},{4,6}}
=> [3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> 2
{{1,3,6},{2},{4},{5}}
=> [3,2,6,4,5,1] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,4,5},{2,3,6}}
=> [4,3,6,5,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,3)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
{{1,4},{2,3,6},{5}}
=> [4,3,6,1,5,2] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,5},{2,3,4,6}}
=> [5,3,4,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
{{1,6},{2,3,4,5}}
=> [6,3,4,5,2,1] => ([(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
{{1,4},{2,5},{3,6}}
=> [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4
{{1,5},{2,6},{3},{4}}
=> [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0
{{1,2,4,6},{3,5,7}}
=> [2,4,5,6,7,1,3] => ([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ? = 3
{{1,2,4},{3,6},{5,7}}
=> [2,4,6,1,7,3,5] => ([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ? = 2
{{1,2,6},{3,7},{4},{5}}
=> [2,6,7,4,5,1,3] => ([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0
{{1,3,5},{2,4,6,7}}
=> [3,4,5,6,1,7,2] => ([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ? = 3
{{1,3,5},{2,4,6},{7}}
=> [3,4,5,6,1,2,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3
{{1,3},{2,4,6},{5,7}}
=> [3,4,1,6,7,2,5] => ([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ? = 2
{{1,3},{2,5},{4,6,7}}
=> [3,5,1,6,2,7,4] => ([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ? = 2
{{1,6},{2,3,4,7},{5}}
=> [6,3,4,7,5,1,2] => ([(0,6),(1,3),(2,4),(4,5),(4,6)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3
{{1,5,6},{2,3,7},{4}}
=> [5,3,7,4,6,1,2] => ([(0,5),(0,6),(1,3),(2,4),(2,5),(4,6)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3
{{1,4,5,6},{2,7},{3}}
=> [4,7,3,5,6,1,2] => ([(0,6),(1,3),(2,4),(2,6),(6,5)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3
{{1,4,7},{2,5},{3,6}}
=> [4,5,6,7,2,3,1] => ([(1,6),(2,4),(5,3),(6,5)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3
{{1,4},{2,5},{3,6},{7}}
=> [4,5,6,1,2,3,7] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4
{{1},{2,4,6},{3,5,7}}
=> [1,4,5,6,7,2,3] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3
{{1,6},{2,7},{3,4,5}}
=> [6,7,4,5,3,1,2] => ([(1,6),(2,5),(3,4)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0
{{1,5},{2,6,7},{3},{4}}
=> [5,6,3,4,1,7,2] => ([(0,5),(1,4),(2,3),(2,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0
{{1,5},{2,6},{3,7},{4}}
=> [5,6,7,4,1,2,3] => ([(1,6),(2,5),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4
{{1,5},{2,6},{3},{4},{7}}
=> [5,6,3,4,1,2,7] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0
{{1,5},{2,7},{3},{4},{6}}
=> [5,7,3,4,1,6,2] => ([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> ? = 0
{{1},{2,5},{3,6},{4,7}}
=> [1,5,6,7,2,3,4] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4
{{1,6},{2},{3,7},{4},{5}}
=> [6,2,7,4,5,1,3] => ([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> ? = 0
{{1},{2,6},{3,7},{4},{5}}
=> [1,6,7,4,5,2,3] => ([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0
{{1,3},{2,5},{4,6},{7,8}}
=> [3,5,1,6,2,4,8,7] => ([(0,3),(0,7),(1,2),(1,6),(2,7),(3,6),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ? = 2
{{1,7},{2,8},{3,4},{5,6}}
=> [7,8,4,3,6,5,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0
{{1,6},{2,8},{3,5},{4,7}}
=> [6,8,5,7,3,1,4,2] => ([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4
{{1,8},{2,5},{3,6},{4,7}}
=> [8,5,6,7,2,3,4,1] => ([(2,5),(3,4),(4,6),(5,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4
{{1,2},{3,5},{4,7},{6,8}}
=> [2,1,5,7,3,8,4,6] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(6,3),(6,5),(7,2),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ? = 2
{{1,3},{2,4},{5,7},{6,8}}
=> [3,4,1,2,7,8,5,6] => ([(0,5),(1,4),(4,6),(4,7),(5,6),(5,7),(6,3),(7,2)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ? = 2
{{1,7},{2,5},{3,8},{4,6}}
=> [7,5,8,6,2,4,1,3] => ([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4
{{1,6},{2,7},{3,8},{4,5}}
=> [6,7,8,5,4,1,2,3] => ([(2,5),(3,4),(4,6),(5,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4
{{1},{2},{3},{4},{5},{6},{7},{8}}
=> [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
=> ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
=> ? = 0
{{1,2,3,5},{4,6,7,8}}
=> [2,3,5,6,1,7,8,4] => ([(0,6),(0,7),(1,5),(3,7),(4,3),(5,4),(5,6),(7,2)],8)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 1
{{1,4,7,8},{2,5},{3,6}}
=> [4,5,6,7,2,3,8,1] => ([(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3
{{1,2,5,8},{3,6},{4,7}}
=> [2,5,6,7,8,3,4,1] => ([(1,6),(1,7),(4,5),(5,3),(6,4),(7,2)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3
{{1,3,7},{2,6,8},{4},{5}}
=> [3,6,7,4,5,8,1,2] => ([(0,4),(1,5),(1,6),(2,7),(3,7),(5,3),(6,2)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0
{{1,4,7},{2,5,8},{3},{6}}
=> [4,5,3,7,8,6,1,2] => ([(0,6),(0,7),(1,3),(2,5),(5,6),(5,7),(7,4)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3
{{1,3,7},{2,5,8},{4},{6}}
=> [3,5,7,4,8,6,1,2] => ([(0,4),(1,3),(1,5),(2,6),(3,6),(3,7),(5,2),(5,7)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3
{{1,2,6},{3,7,8},{4},{5}}
=> [2,6,7,4,5,1,8,3] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(2,7),(3,7),(4,3),(5,2)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0
{{1,4,8},{2,5},{3,6},{7}}
=> [4,5,6,8,2,3,7,1] => ([(1,6),(2,4),(4,7),(5,3),(5,7),(6,5)],8)
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ? = 3
{{1,4,7},{2,5},{3,6},{8}}
=> [4,5,6,7,2,3,1,8] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3
{{1,5},{2,6},{3,7},{4},{8}}
=> [5,6,7,4,1,2,3,8] => ([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4
{{1},{2,5,8},{3,6},{4,7}}
=> [1,5,6,7,8,3,4,2] => ([(0,3),(0,6),(0,7),(4,5),(5,2),(6,4),(7,1)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3
{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
=> [1,2,3,4,5,6,7,8,9] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
=> ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
=> ? = 0
{{1,2,3,4,5,6,7,8,9},{10}}
=> [2,3,4,5,6,7,8,9,1,10] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
=> ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
=> ? = 0
{{1},{2,3,4,5,6,7,8,9,10}}
=> [1,3,4,5,6,7,8,9,10,2] => ([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
=> ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
=> ? = 0
{{1,5},{2,6,8},{3},{4,7}}
=> [5,6,3,7,1,8,4,2] => ([(0,5),(0,7),(1,4),(2,3),(2,5),(2,6),(4,7),(7,6)],8)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ? = 2
{{1,5,6,7},{2,3,4,8}}
=> [5,3,4,8,6,7,1,2] => ([(0,6),(0,7),(1,3),(2,5),(5,6),(5,7),(7,4)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3
{{1},{2,5,6,7},{3,8},{4}}
=> [1,5,8,4,6,7,2,3] => ([(0,4),(0,5),(0,6),(4,7),(5,2),(6,1),(6,7),(7,3)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3
Description
Number of indecomposable injective modules with projective dimension 2.
Matching statistic: St001597
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
St001597: Skew partitions ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 40%
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
St001597: Skew partitions ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 40%
Values
{{1},{2},{3}}
=> [1,2,3] => [1,0,1,0,1,0]
=> [[1,1,1],[]]
=> 1 = 0 + 1
{{1,2,3,4}}
=> [2,3,4,1] => [1,1,0,1,0,1,0,0]
=> [[4],[]]
=> 1 = 0 + 1
{{1,3},{2,4}}
=> [3,4,1,2] => [1,1,1,0,1,0,0,0]
=> [[2,2,2],[]]
=> 2 = 1 + 1
{{1},{2},{3},{4}}
=> [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,1,1,1],[]]
=> 1 = 0 + 1
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0]
=> [[5],[]]
=> 1 = 0 + 1
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
=> [[4,4],[3]]
=> 1 = 0 + 1
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0]
=> [[4,3],[2]]
=> 1 = 0 + 1
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3],[1,1]]
=> 2 = 1 + 1
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0]
=> [[4,2],[1]]
=> 1 = 0 + 1
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0]
=> [[2,2,2,2],[]]
=> ? = 0 + 1
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0]
=> [[3,2,2],[]]
=> 2 = 1 + 1
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0]
=> [[2,2,2,2],[1]]
=> 2 = 1 + 1
{{1},{2,3,4,5}}
=> [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
=> [[4,1],[]]
=> 1 = 0 + 1
{{1,4},{2,5},{3}}
=> [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
=> [[4,4],[]]
=> ? = 1 + 1
{{1},{2,4},{3,5}}
=> [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
=> [[2,2,2,1],[]]
=> 2 = 1 + 1
{{1,5},{2},{3},{4}}
=> [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3],[]]
=> ? = 0 + 1
{{1},{2},{3},{4},{5}}
=> [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [[1,1,1,1,1],[]]
=> 1 = 0 + 1
{{1,2,3,4,5,6}}
=> [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0]
=> [[6],[]]
=> 1 = 0 + 1
{{1,2,3,4,5},{6}}
=> [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0]
=> [[5,5],[4]]
=> 1 = 0 + 1
{{1,2,3,4},{5,6}}
=> [2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0]
=> [[5,4],[3]]
=> 1 = 0 + 1
{{1,2,3,4},{5},{6}}
=> [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0]
=> [[4,4,4],[3,3]]
=> 1 = 0 + 1
{{1,2,3,5},{4,6}}
=> [2,3,5,6,1,4] => [1,1,0,1,0,1,1,0,1,0,0,0]
=> [[4,4,4],[2,2]]
=> ? = 1 + 1
{{1,2,3},{4,5,6}}
=> [2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0]
=> [[5,3],[2]]
=> 1 = 0 + 1
{{1,2,3},{4,5},{6}}
=> [2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0]
=> [[4,4,3],[3,2]]
=> 1 = 0 + 1
{{1,2,3},{4},{5,6}}
=> [2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0]
=> [[4,3,3],[2,2]]
=> 1 = 0 + 1
{{1,2,4,6},{3,5}}
=> [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0]
=> [[3,3,3,3],[1,1,1]]
=> ? = 0 + 1
{{1,2,4},{3,5,6}}
=> [2,4,5,1,6,3] => [1,1,0,1,1,0,1,0,0,1,0,0]
=> [[4,3,3],[1,1]]
=> ? = 1 + 1
{{1,2,4},{3,5},{6}}
=> [2,4,5,1,3,6] => [1,1,0,1,1,0,1,0,0,0,1,0]
=> [[3,3,3,3],[2,1,1]]
=> ? = 1 + 1
{{1,2},{3,4,5,6}}
=> [2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0]
=> [[5,2],[1]]
=> 1 = 0 + 1
{{1,2},{3,4,5},{6}}
=> [2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0]
=> [[4,4,2],[3,1]]
=> 1 = 0 + 1
{{1,2},{3,4},{5,6}}
=> [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0]
=> [[4,3,2],[2,1]]
=> 1 = 0 + 1
{{1,2,5},{3,6},{4}}
=> [2,5,6,4,1,3] => [1,1,0,1,1,1,0,1,0,0,0,0]
=> [[5,5],[1]]
=> ? = 1 + 1
{{1,2},{3,5},{4,6}}
=> [2,1,5,6,3,4] => [1,1,0,0,1,1,1,0,1,0,0,0]
=> [[3,3,3,2],[1,1,1]]
=> ? = 1 + 1
{{1,2},{3},{4,5,6}}
=> [2,1,3,5,6,4] => [1,1,0,0,1,0,1,1,0,1,0,0]
=> [[4,2,2],[1,1]]
=> 1 = 0 + 1
{{1,2,6},{3},{4},{5}}
=> [2,6,3,4,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0]
=> [[4,4,4],[1,1]]
=> ? = 0 + 1
{{1,3,4,5},{2,6}}
=> [3,6,4,5,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
=> [[3,3,3,2],[]]
=> ? = 1 + 1
{{1,3,4},{2,6},{5}}
=> [3,6,4,1,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
=> [[3,3,3,2],[]]
=> ? = 0 + 1
{{1,3,5,6},{2,4}}
=> [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0]
=> [[3,2,2,2],[]]
=> ? = 0 + 1
{{1,3,5},{2,4,6}}
=> [3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0]
=> [[2,2,2,2,2],[]]
=> ? = 3 + 1
{{1,3,5},{2,4},{6}}
=> [3,4,5,2,1,6] => [1,1,1,0,1,0,1,0,0,0,1,0]
=> [[2,2,2,2,2],[1]]
=> ? = 0 + 1
{{1,3},{2,4,5,6}}
=> [3,4,1,5,6,2] => [1,1,1,0,1,0,0,1,0,1,0,0]
=> [[4,2,2],[]]
=> ? = 1 + 1
{{1,3},{2,4,5},{6}}
=> [3,4,1,5,2,6] => [1,1,1,0,1,0,0,1,0,0,1,0]
=> [[3,3,2,2],[2]]
=> ? = 1 + 1
{{1,3,6},{2,4},{5}}
=> [3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0]
=> [[3,3,2,2],[]]
=> ? = 0 + 1
{{1,3},{2,4},{5,6}}
=> [3,4,1,2,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0]
=> [[3,2,2,2],[1]]
=> ? = 1 + 1
{{1,3},{2,4},{5},{6}}
=> [3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
=> [[2,2,2,2,2],[1,1]]
=> ? = 1 + 1
{{1,3},{2,5},{4,6}}
=> [3,5,1,6,2,4] => [1,1,1,0,1,1,0,0,1,0,0,0]
=> [[3,3,3,2],[1]]
=> ? = 2 + 1
{{1,3,6},{2},{4},{5}}
=> [3,2,6,4,5,1] => [1,1,1,0,0,1,1,1,0,0,0,0]
=> [[4,4,2],[1]]
=> ? = 0 + 1
{{1,4,5},{2,3,6}}
=> [4,3,6,5,1,2] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> [[4,4,3],[1]]
=> ? = 1 + 1
{{1,4},{2,3,6},{5}}
=> [4,3,6,1,5,2] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> [[4,4,3],[1]]
=> ? = 0 + 1
{{1,5},{2,3,4,6}}
=> [5,3,4,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> [[3,3,3,3],[1]]
=> ? = 1 + 1
{{1,6},{2,3,4,5}}
=> [6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [[4,4,4],[]]
=> ? = 0 + 1
{{1},{2,3,4,5,6}}
=> [1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0]
=> [[5,1],[]]
=> 1 = 0 + 1
{{1},{2,3,4,5},{6}}
=> [1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0]
=> [[4,4,1],[3]]
=> 1 = 0 + 1
{{1},{2,3,4},{5,6}}
=> [1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1],[2]]
=> 1 = 0 + 1
{{1,5},{2,3,6},{4}}
=> [5,3,6,4,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> [[4,4,3],[]]
=> ? = 2 + 1
{{1},{2,3,5},{4,6}}
=> [1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3,1],[1,1]]
=> ? = 1 + 1
{{1},{2,3},{4,5,6}}
=> [1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0]
=> [[4,2,1],[1]]
=> 1 = 0 + 1
{{1,4,5},{2,6},{3}}
=> [4,6,3,5,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
=> [[4,4,4],[1]]
=> ? = 2 + 1
{{1,4,5},{2},{3,6}}
=> [4,2,6,5,1,3] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> [[4,4,3],[1]]
=> ? = 0 + 1
{{1,4},{2,5,6},{3}}
=> [4,5,3,1,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0]
=> [[5,4],[]]
=> ? = 1 + 1
{{1,4},{2,5},{3,6}}
=> [4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0]
=> [[5,5],[]]
=> ? = 4 + 1
{{1,4},{2,5},{3},{6}}
=> [4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0]
=> [[4,4,4],[3]]
=> ? = 1 + 1
{{1,4,6},{2},{3,5}}
=> [4,2,5,6,3,1] => [1,1,1,1,0,0,1,0,1,0,0,0]
=> [[3,3,3,3],[1,1]]
=> ? = 0 + 1
{{1,4,6},{2},{3},{5}}
=> [4,2,3,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0]
=> [[4,4,3],[2]]
=> ? = 0 + 1
{{1,4},{2,6},{3},{5}}
=> [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
=> [[4,4,4],[1]]
=> ? = 1 + 1
{{1,6},{2,4},{3,5}}
=> [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [[4,4,4],[]]
=> ? = 1 + 1
{{1},{2,4,6},{3,5}}
=> [1,4,5,6,3,2] => [1,0,1,1,1,0,1,0,1,0,0,0]
=> [[2,2,2,2,1],[]]
=> ? = 0 + 1
{{1},{2,4},{3,5,6}}
=> [1,4,5,2,6,3] => [1,0,1,1,1,0,1,0,0,1,0,0]
=> [[3,2,2,1],[]]
=> ? = 1 + 1
{{1},{2,4},{3,5},{6}}
=> [1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0]
=> [[2,2,2,2,1],[1]]
=> ? = 1 + 1
{{1,5},{2,6},{3,4}}
=> [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> [[3,3,3,3],[]]
=> ? = 1 + 1
{{1,5},{2},{3,4,6}}
=> [5,2,4,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> [[3,3,3,3],[1]]
=> ? = 0 + 1
{{1},{2},{3,4,5,6}}
=> [1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0]
=> [[4,1,1],[]]
=> 1 = 0 + 1
{{1,5,6},{2},{3},{4}}
=> [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0]
=> [[4,3,3],[]]
=> ? = 0 + 1
{{1,5},{2,6},{3},{4}}
=> [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> [[3,3,3,3],[]]
=> ? = 0 + 1
{{1,5},{2},{3,6},{4}}
=> [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> [[4,4,3],[]]
=> ? = 1 + 1
{{1,5},{2},{3},{4},{6}}
=> [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> [[3,3,3,3],[2]]
=> ? = 0 + 1
{{1},{2,5},{3,6},{4}}
=> [1,5,6,4,2,3] => [1,0,1,1,1,1,0,1,0,0,0,0]
=> [[4,4,1],[]]
=> ? = 1 + 1
{{1},{2},{3,5},{4,6}}
=> [1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0]
=> [[2,2,2,1,1],[]]
=> ? = 1 + 1
{{1,6},{2},{3},{4},{5}}
=> [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [[4,4,4],[]]
=> ? = 0 + 1
{{1},{2,6},{3},{4},{5}}
=> [1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3,1],[]]
=> ? = 0 + 1
{{1},{2},{3},{4},{5},{6}}
=> [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
=> [[1,1,1,1,1,1],[]]
=> 1 = 0 + 1
{{1,2,3,4,5,6,7}}
=> [2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [[7],[]]
=> 1 = 0 + 1
{{1,2,3,4,5,6},{7}}
=> [2,3,4,5,6,1,7] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [[6,6],[5]]
=> 1 = 0 + 1
{{1,2,3,4,5},{6,7}}
=> [2,3,4,5,1,7,6] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0]
=> [[6,5],[4]]
=> 1 = 0 + 1
{{1,2,3,4,5},{6},{7}}
=> [2,3,4,5,1,6,7] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
=> [[5,5,5],[4,4]]
=> 1 = 0 + 1
{{1,2,3,4},{5,6,7}}
=> [2,3,4,1,6,7,5] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0]
=> [[6,4],[3]]
=> 1 = 0 + 1
{{1,2,3,4},{5,6},{7}}
=> [2,3,4,1,6,5,7] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0]
=> [[5,5,4],[4,3]]
=> 1 = 0 + 1
{{1,2,3,4},{5},{6,7}}
=> [2,3,4,1,5,7,6] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0]
=> [[5,4,4],[3,3]]
=> 1 = 0 + 1
{{1,2,3,4},{5},{6},{7}}
=> [2,3,4,1,5,6,7] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=> [[4,4,4,4],[3,3,3]]
=> 1 = 0 + 1
{{1,2,3},{4,5,6,7}}
=> [2,3,1,5,6,7,4] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0]
=> [[6,3],[2]]
=> 1 = 0 + 1
{{1,2,3},{4,5,6},{7}}
=> [2,3,1,5,6,4,7] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0]
=> [[5,5,3],[4,2]]
=> 1 = 0 + 1
{{1,2,3},{4,5},{6,7}}
=> [2,3,1,5,4,7,6] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0]
=> [[5,4,3],[3,2]]
=> 1 = 0 + 1
{{1,2,3},{4,5},{6},{7}}
=> [2,3,1,5,4,6,7] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0]
=> [[4,4,4,3],[3,3,2]]
=> 1 = 0 + 1
{{1,2,3},{4},{5,6,7}}
=> [2,3,1,4,6,7,5] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0]
=> [[5,3,3],[2,2]]
=> 1 = 0 + 1
{{1,2,3},{4},{5,6},{7}}
=> [2,3,1,4,6,5,7] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0]
=> [[4,4,3,3],[3,2,2]]
=> 1 = 0 + 1
{{1,2,3},{4},{5},{6,7}}
=> [2,3,1,4,5,7,6] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0]
=> [[4,3,3,3],[2,2,2]]
=> 1 = 0 + 1
{{1,2},{3,4,5,6,7}}
=> [2,1,4,5,6,7,3] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0]
=> [[6,2],[1]]
=> 1 = 0 + 1
{{1,2},{3,4,5,6},{7}}
=> [2,1,4,5,6,3,7] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0]
=> [[5,5,2],[4,1]]
=> 1 = 0 + 1
{{1,2},{3,4,5},{6,7}}
=> [2,1,4,5,3,7,6] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0]
=> [[5,4,2],[3,1]]
=> 1 = 0 + 1
{{1,2},{3,4,5},{6},{7}}
=> [2,1,4,5,3,6,7] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0]
=> [[4,4,4,2],[3,3,1]]
=> 1 = 0 + 1
Description
The Frobenius rank of a skew partition.
This is the minimal number of border strips in a border strip decomposition of the skew partition.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!