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Matching statistic: St001780
St001780: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 1
[2]
=> 1
[1,1]
=> 1
[3]
=> 1
[2,1]
=> 2
[1,1,1]
=> 1
[4]
=> 1
[3,1]
=> 3
[2,2]
=> 2
[2,1,1]
=> 3
[1,1,1,1]
=> 1
[5]
=> 1
[4,1]
=> 4
[3,2]
=> 6
[3,1,1]
=> 4
[2,2,1]
=> 6
[2,1,1,1]
=> 4
[1,1,1,1,1]
=> 1
[6]
=> 1
[5,1]
=> 5
[4,2]
=> 20
[4,1,1]
=> 5
[3,3]
=> 6
[3,2,1]
=> 12
[3,1,1,1]
=> 5
[2,2,2]
=> 6
[2,2,1,1]
=> 20
[2,1,1,1,1]
=> 5
[1,1,1,1,1,1]
=> 1
[7]
=> 1
[6,1]
=> 6
[5,2]
=> 30
[5,1,1]
=> 6
[4,3]
=> 8
[4,2,1]
=> 260
[4,1,1,1]
=> 6
[3,3,1]
=> 195
[3,2,2]
=> 195
[3,2,1,1]
=> 260
[3,1,1,1,1]
=> 6
[2,2,2,1]
=> 8
[2,2,1,1,1]
=> 30
[2,1,1,1,1,1]
=> 6
[1,1,1,1,1,1,1]
=> 1
[8]
=> 1
[7,1]
=> 7
[6,2]
=> 42
[6,1,1]
=> 7
[5,3]
=> 560
[5,2,1]
=> 924
Description
The order of promotion on the set of standard tableaux of given shape.
Matching statistic: St001779
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St001779: Posets ⟶ ℤResult quality: 18% ●values known / values provided: 21%●distinct values known / distinct values provided: 18%
Mp00185: Skew partitions —cell poset⟶ Posets
St001779: Posets ⟶ ℤResult quality: 18% ●values known / values provided: 21%●distinct values known / distinct values provided: 18%
Values
[1]
=> [[1],[]]
=> ([],1)
=> 1
[2]
=> [[2],[]]
=> ([(0,1)],2)
=> 1
[1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> 1
[3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 1
[2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> 2
[1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 1
[4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> 3
[2,2]
=> [[2,2],[]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> 3
[1,1,1,1]
=> [[1,1,1,1],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[5]
=> [[5],[]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[4,1]
=> [[4,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 4
[3,2]
=> [[3,2],[]]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> 6
[3,1,1]
=> [[3,1,1],[]]
=> ([(0,3),(0,4),(3,2),(4,1)],5)
=> 4
[2,2,1]
=> [[2,2,1],[]]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> 6
[2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 4
[1,1,1,1,1]
=> [[1,1,1,1,1],[]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[6]
=> [[6],[]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1
[5,1]
=> [[5,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 5
[4,2]
=> [[4,2],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 20
[4,1,1]
=> [[4,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 5
[3,3]
=> [[3,3],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[3,2,1]
=> [[3,2,1],[]]
=> ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> 12
[3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 5
[2,2,2]
=> [[2,2,2],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 20
[2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 5
[1,1,1,1,1,1]
=> [[1,1,1,1,1,1],[]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1
[7]
=> [[7],[]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260}
[6,1]
=> [[6,1],[]]
=> ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260}
[5,2]
=> [[5,2],[]]
=> ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260}
[5,1,1]
=> [[5,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260}
[4,3]
=> [[4,3],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260}
[4,2,1]
=> [[4,2,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260}
[4,1,1,1]
=> [[4,1,1,1],[]]
=> ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260}
[3,3,1]
=> [[3,3,1],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260}
[3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260}
[3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260}
[3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260}
[2,2,2,1]
=> [[2,2,2,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260}
[2,2,1,1,1]
=> [[2,2,1,1,1],[]]
=> ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260}
[2,1,1,1,1,1]
=> [[2,1,1,1,1,1],[]]
=> ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260}
[1,1,1,1,1,1,1]
=> [[1,1,1,1,1,1,1],[]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260}
[8]
=> [[8],[]]
=> ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[7,1]
=> [[7,1],[]]
=> ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[6,2]
=> [[6,2],[]]
=> ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[6,1,1]
=> [[6,1,1],[]]
=> ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[5,3]
=> [[5,3],[]]
=> ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[5,2,1]
=> [[5,2,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[5,1,1,1]
=> [[5,1,1,1],[]]
=> ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[4,4]
=> [[4,4],[]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[4,3,1]
=> [[4,3,1],[]]
=> ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[4,2,2]
=> [[4,2,2],[]]
=> ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[4,2,1,1]
=> [[4,2,1,1],[]]
=> ([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[4,1,1,1,1]
=> [[4,1,1,1,1],[]]
=> ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[3,3,2]
=> [[3,3,2],[]]
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[3,3,1,1]
=> [[3,3,1,1],[]]
=> ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[3,2,2,1]
=> [[3,2,2,1],[]]
=> ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[3,2,1,1,1]
=> [[3,2,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[3,1,1,1,1,1]
=> [[3,1,1,1,1,1],[]]
=> ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[2,2,2,2]
=> [[2,2,2,2],[]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[2,2,2,1,1]
=> [[2,2,2,1,1],[]]
=> ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[2,2,1,1,1,1]
=> [[2,2,1,1,1,1],[]]
=> ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[2,1,1,1,1,1,1]
=> [[2,1,1,1,1,1,1],[]]
=> ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[1,1,1,1,1,1,1,1]
=> [[1,1,1,1,1,1,1,1],[]]
=> ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924}
[9]
=> [[9],[]]
=> ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
=> ? ∊ {1,1,8,8,8,8,8,8,8,9,10,10,56,56,252,252,312,312,1848,1848,3696,3696,6188,6188,26400,26400,32760,32760,308154,308154}
[8,1]
=> [[8,1],[]]
=> ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9)
=> ? ∊ {1,1,8,8,8,8,8,8,8,9,10,10,56,56,252,252,312,312,1848,1848,3696,3696,6188,6188,26400,26400,32760,32760,308154,308154}
[7,2]
=> [[7,2],[]]
=> ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9)
=> ? ∊ {1,1,8,8,8,8,8,8,8,9,10,10,56,56,252,252,312,312,1848,1848,3696,3696,6188,6188,26400,26400,32760,32760,308154,308154}
[7,1,1]
=> [[7,1,1],[]]
=> ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9)
=> ? ∊ {1,1,8,8,8,8,8,8,8,9,10,10,56,56,252,252,312,312,1848,1848,3696,3696,6188,6188,26400,26400,32760,32760,308154,308154}
[6,3]
=> [[6,3],[]]
=> ([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9)
=> ? ∊ {1,1,8,8,8,8,8,8,8,9,10,10,56,56,252,252,312,312,1848,1848,3696,3696,6188,6188,26400,26400,32760,32760,308154,308154}
[6,2,1]
=> [[6,2,1],[]]
=> ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9)
=> ? ∊ {1,1,8,8,8,8,8,8,8,9,10,10,56,56,252,252,312,312,1848,1848,3696,3696,6188,6188,26400,26400,32760,32760,308154,308154}
[6,1,1,1]
=> [[6,1,1,1],[]]
=> ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9)
=> ? ∊ {1,1,8,8,8,8,8,8,8,9,10,10,56,56,252,252,312,312,1848,1848,3696,3696,6188,6188,26400,26400,32760,32760,308154,308154}
[5,4]
=> [[5,4],[]]
=> ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9)
=> ? ∊ {1,1,8,8,8,8,8,8,8,9,10,10,56,56,252,252,312,312,1848,1848,3696,3696,6188,6188,26400,26400,32760,32760,308154,308154}
[5,3,1]
=> [[5,3,1],[]]
=> ([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9)
=> ? ∊ {1,1,8,8,8,8,8,8,8,9,10,10,56,56,252,252,312,312,1848,1848,3696,3696,6188,6188,26400,26400,32760,32760,308154,308154}
[5,2,2]
=> [[5,2,2],[]]
=> ([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9)
=> ? ∊ {1,1,8,8,8,8,8,8,8,9,10,10,56,56,252,252,312,312,1848,1848,3696,3696,6188,6188,26400,26400,32760,32760,308154,308154}
[5,2,1,1]
=> [[5,2,1,1],[]]
=> ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9)
=> ? ∊ {1,1,8,8,8,8,8,8,8,9,10,10,56,56,252,252,312,312,1848,1848,3696,3696,6188,6188,26400,26400,32760,32760,308154,308154}
[5,1,1,1,1]
=> [[5,1,1,1,1],[]]
=> ([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(8,4)],9)
=> ? ∊ {1,1,8,8,8,8,8,8,8,9,10,10,56,56,252,252,312,312,1848,1848,3696,3696,6188,6188,26400,26400,32760,32760,308154,308154}
[4,4,1]
=> [[4,4,1],[]]
=> ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9)
=> ? ∊ {1,1,8,8,8,8,8,8,8,9,10,10,56,56,252,252,312,312,1848,1848,3696,3696,6188,6188,26400,26400,32760,32760,308154,308154}
Description
The order of promotion on the set of linear extensions of a poset.
Matching statistic: St001877
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
Mp00195: Posets —order ideals⟶ Lattices
St001877: Lattices ⟶ ℤResult quality: 7% ●values known / values provided: 10%●distinct values known / distinct values provided: 7%
Mp00185: Skew partitions —cell poset⟶ Posets
Mp00195: Posets —order ideals⟶ Lattices
St001877: Lattices ⟶ ℤResult quality: 7% ●values known / values provided: 10%●distinct values known / distinct values provided: 7%
Values
[1]
=> [[1],[]]
=> ([],1)
=> ([(0,1)],2)
=> ? = 1 - 1
[2]
=> [[2],[]]
=> ([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> 0 = 1 - 1
[1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> 0 = 1 - 1
[3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> 0 = 1 - 1
[2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1 = 2 - 1
[1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> 0 = 1 - 1
[4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0 = 1 - 1
[3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> 2 = 3 - 1
[2,2]
=> [[2,2],[]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 1 = 2 - 1
[2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> 2 = 3 - 1
[1,1,1,1]
=> [[1,1,1,1],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0 = 1 - 1
[5]
=> [[5],[]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 1 - 1
[4,1]
=> [[4,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ? ∊ {4,4,4,6,6} - 1
[3,2]
=> [[3,2],[]]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ? ∊ {4,4,4,6,6} - 1
[3,1,1]
=> [[3,1,1],[]]
=> ([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(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)
=> ? ∊ {4,4,4,6,6} - 1
[2,2,1]
=> [[2,2,1],[]]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ? ∊ {4,4,4,6,6} - 1
[2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ? ∊ {4,4,4,6,6} - 1
[1,1,1,1,1]
=> [[1,1,1,1,1],[]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 1 - 1
[6]
=> [[6],[]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 0 = 1 - 1
[5,1]
=> [[5,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,5),(4,10),(5,2),(5,9),(6,1),(6,3),(7,10),(9,8),(10,9)],11)
=> ? ∊ {5,5,5,5,6,6,12,20,20} - 1
[4,2]
=> [[4,2],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12)
=> ? ∊ {5,5,5,5,6,6,12,20,20} - 1
[4,1,1]
=> [[4,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13)
=> ? ∊ {5,5,5,5,6,6,12,20,20} - 1
[3,3]
=> [[3,3],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
=> ? ∊ {5,5,5,5,6,6,12,20,20} - 1
[3,2,1]
=> [[3,2,1],[]]
=> ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14)
=> ? ∊ {5,5,5,5,6,6,12,20,20} - 1
[3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13)
=> ? ∊ {5,5,5,5,6,6,12,20,20} - 1
[2,2,2]
=> [[2,2,2],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
=> ? ∊ {5,5,5,5,6,6,12,20,20} - 1
[2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12)
=> ? ∊ {5,5,5,5,6,6,12,20,20} - 1
[2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,5),(4,10),(5,2),(5,9),(6,1),(6,3),(7,10),(9,8),(10,9)],11)
=> ? ∊ {5,5,5,5,6,6,12,20,20} - 1
[1,1,1,1,1,1]
=> [[1,1,1,1,1,1],[]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 0 = 1 - 1
[7]
=> [[7],[]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260} - 1
[6,1]
=> [[6,1],[]]
=> ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
=> ([(0,7),(1,8),(2,9),(3,5),(3,8),(4,6),(4,10),(5,4),(5,12),(6,2),(6,11),(7,1),(7,3),(8,12),(10,11),(11,9),(12,10)],13)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260} - 1
[5,2]
=> [[5,2],[]]
=> ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)
=> ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260} - 1
[5,1,1]
=> [[5,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,1),(1,2),(1,3),(2,5),(2,13),(3,7),(3,13),(4,12),(5,11),(6,4),(6,15),(7,6),(7,14),(9,10),(10,8),(11,9),(12,8),(13,11),(13,14),(14,9),(14,15),(15,10),(15,12)],16)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260} - 1
[4,3]
=> [[4,3],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)
=> ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260} - 1
[4,2,1]
=> [[4,2,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260} - 1
[4,1,1,1]
=> [[4,1,1,1],[]]
=> ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ([(0,1),(1,2),(1,3),(2,7),(2,14),(3,6),(3,14),(4,11),(5,12),(6,4),(6,15),(7,5),(7,16),(9,8),(10,8),(11,9),(12,10),(13,9),(13,10),(14,15),(14,16),(15,11),(15,13),(16,12),(16,13)],17)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260} - 1
[3,3,1]
=> [[3,3,1],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260} - 1
[3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260} - 1
[3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260} - 1
[3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,1),(1,2),(1,3),(2,5),(2,13),(3,7),(3,13),(4,12),(5,11),(6,4),(6,15),(7,6),(7,14),(9,10),(10,8),(11,9),(12,8),(13,11),(13,14),(14,9),(14,15),(15,10),(15,12)],16)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260} - 1
[2,2,2,1]
=> [[2,2,2,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)
=> ([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260} - 1
[2,2,1,1,1]
=> [[2,2,1,1,1],[]]
=> ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)
=> ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260} - 1
[2,1,1,1,1,1]
=> [[2,1,1,1,1,1],[]]
=> ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
=> ([(0,7),(1,8),(2,9),(3,5),(3,8),(4,6),(4,10),(5,4),(5,12),(6,2),(6,11),(7,1),(7,3),(8,12),(10,11),(11,9),(12,10)],13)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260} - 1
[1,1,1,1,1,1,1]
=> [[1,1,1,1,1,1,1],[]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
=> ? ∊ {1,1,6,6,6,6,6,8,8,30,30,195,195,260,260} - 1
[8]
=> [[8],[]]
=> ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
=> ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[7,1]
=> [[7,1],[]]
=> ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)
=> ([(0,8),(1,9),(2,10),(3,6),(3,9),(4,5),(4,12),(5,7),(5,11),(6,4),(6,14),(7,2),(7,13),(8,1),(8,3),(9,14),(11,13),(12,11),(13,10),(14,12)],15)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[6,2]
=> [[6,2],[]]
=> ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8)
=> ([(0,1),(1,3),(1,4),(2,12),(3,10),(4,6),(4,10),(5,14),(6,7),(6,15),(7,8),(7,17),(8,5),(8,16),(10,2),(10,15),(11,13),(12,11),(13,9),(14,9),(15,12),(15,17),(16,13),(16,14),(17,11),(17,16)],18)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[6,1,1]
=> [[6,1,1],[]]
=> ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)
=> ([(0,1),(1,2),(1,3),(2,5),(2,15),(3,6),(3,15),(4,14),(5,13),(6,7),(6,16),(7,8),(7,18),(8,4),(8,17),(10,12),(11,10),(12,9),(13,11),(14,9),(15,13),(15,16),(16,11),(16,18),(17,12),(17,14),(18,10),(18,17)],19)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[5,3]
=> [[5,3],[]]
=> ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8)
=> ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[5,2,1]
=> [[5,2,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)
=> ?
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[5,1,1,1]
=> [[5,1,1,1],[]]
=> ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)
=> ?
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[4,4]
=> [[4,4],[]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[4,3,1]
=> [[4,3,1],[]]
=> ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
=> ?
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[4,2,2]
=> [[4,2,2],[]]
=> ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
=> ?
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[4,2,1,1]
=> [[4,2,1,1],[]]
=> ([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8)
=> ?
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[4,1,1,1,1]
=> [[4,1,1,1,1],[]]
=> ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)
=> ?
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[3,3,2]
=> [[3,3,2],[]]
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8)
=> ([(0,1),(1,4),(1,5),(2,14),(3,13),(4,6),(4,17),(5,7),(5,17),(6,15),(7,16),(8,11),(8,12),(10,18),(11,3),(11,18),(12,2),(12,18),(13,9),(14,9),(15,10),(15,11),(16,10),(16,12),(17,8),(17,15),(17,16),(18,13),(18,14)],19)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[3,3,1,1]
=> [[3,3,1,1],[]]
=> ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
=> ?
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[3,2,2,1]
=> [[3,2,2,1],[]]
=> ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
=> ?
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[3,2,1,1,1]
=> [[3,2,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)
=> ?
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[3,1,1,1,1,1]
=> [[3,1,1,1,1,1],[]]
=> ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)
=> ([(0,1),(1,2),(1,3),(2,5),(2,15),(3,6),(3,15),(4,14),(5,13),(6,7),(6,16),(7,8),(7,18),(8,4),(8,17),(10,12),(11,10),(12,9),(13,11),(14,9),(15,13),(15,16),(16,11),(16,18),(17,12),(17,14),(18,10),(18,17)],19)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[2,2,2,2]
=> [[2,2,2,2],[]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[2,2,2,1,1]
=> [[2,2,2,1,1],[]]
=> ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8)
=> ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
[2,2,1,1,1,1]
=> [[2,2,1,1,1,1],[]]
=> ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8)
=> ([(0,1),(1,3),(1,4),(2,12),(3,10),(4,6),(4,10),(5,14),(6,7),(6,15),(7,8),(7,17),(8,5),(8,16),(10,2),(10,15),(11,13),(12,11),(13,9),(14,9),(15,12),(15,17),(16,13),(16,14),(17,11),(17,16)],18)
=> ? ∊ {1,1,7,7,7,7,7,7,8,8,9,42,42,352,352,462,462,560,560,660,924,924} - 1
Description
Number of indecomposable injective modules with projective dimension 2.
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