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Your data matches 7 different statistics following compositions of up to 3 maps.
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Matching statistic: St000417
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St000417: Ordered trees ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[],[]]
=> 2
[[[]]]
=> 1
[[],[],[]]
=> 6
[[],[[]]]
=> 1
[[[]],[]]
=> 1
[[[],[]]]
=> 2
[[[[]]]]
=> 1
[[],[],[],[]]
=> 24
[[],[],[[]]]
=> 2
[[],[[]],[]]
=> 2
[[],[[],[]]]
=> 2
[[],[[[]]]]
=> 1
[[[]],[],[]]
=> 2
[[[]],[[]]]
=> 2
[[[],[]],[]]
=> 2
[[[[]]],[]]
=> 1
[[[],[],[]]]
=> 6
[[[],[[]]]]
=> 1
[[[[]],[]]]
=> 1
[[[[],[]]]]
=> 2
[[[[[]]]]]
=> 1
[[],[],[],[],[]]
=> 120
[[],[],[],[[]]]
=> 6
[[],[],[[]],[]]
=> 6
[[],[],[[],[]]]
=> 4
[[],[],[[[]]]]
=> 2
[[],[[]],[],[]]
=> 6
[[],[[]],[[]]]
=> 2
[[],[[],[]],[]]
=> 4
[[],[[[]]],[]]
=> 2
[[],[[],[],[]]]
=> 6
[[],[[],[[]]]]
=> 1
[[],[[[]],[]]]
=> 1
[[],[[[],[]]]]
=> 2
[[],[[[[]]]]]
=> 1
[[[]],[],[],[]]
=> 6
[[[]],[],[[]]]
=> 2
[[[]],[[]],[]]
=> 2
[[[]],[[],[]]]
=> 2
[[[]],[[[]]]]
=> 1
[[[],[]],[],[]]
=> 4
[[[[]]],[],[]]
=> 2
[[[],[]],[[]]]
=> 2
[[[[]]],[[]]]
=> 1
[[[],[],[]],[]]
=> 6
[[[],[[]]],[]]
=> 1
[[[[]],[]],[]]
=> 1
[[[[],[]]],[]]
=> 2
[[[[[]]]],[]]
=> 1
[[[],[],[],[]]]
=> 24
Description
The size of the automorphism group of the ordered tree.
Matching statistic: St000633
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(load all 3 compositions to match this statistic)
Mp00139: Ordered trees —Zeilberger's Strahler bijection⟶ Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000633: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000633: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[],[]]
=> [.,[.,.]]
=> [2,1] => ([],2)
=> 2
[[[]]]
=> [[.,.],.]
=> [1,2] => ([(0,1)],2)
=> 1
[[],[],[]]
=> [.,[.,[.,.]]]
=> [3,2,1] => ([],3)
=> 6
[[],[[]]]
=> [.,[[.,.],.]]
=> [2,3,1] => ([(1,2)],3)
=> 1
[[[]],[]]
=> [[.,[.,.]],.]
=> [2,1,3] => ([(0,2),(1,2)],3)
=> 2
[[[],[]]]
=> [[.,.],[.,.]]
=> [3,1,2] => ([(1,2)],3)
=> 1
[[[[]]]]
=> [[[.,.],.],.]
=> [1,2,3] => ([(0,2),(2,1)],3)
=> 1
[[],[],[],[]]
=> [.,[.,[.,[.,.]]]]
=> [4,3,2,1] => ([],4)
=> 24
[[],[],[[]]]
=> [.,[.,[[.,.],.]]]
=> [3,4,2,1] => ([(2,3)],4)
=> 2
[[],[[]],[]]
=> [.,[[.,[.,.]],.]]
=> [3,2,4,1] => ([(1,3),(2,3)],4)
=> 2
[[],[[],[]]]
=> [.,[[.,.],[.,.]]]
=> [4,2,3,1] => ([(2,3)],4)
=> 2
[[],[[[]]]]
=> [.,[[[.,.],.],.]]
=> [2,3,4,1] => ([(1,2),(2,3)],4)
=> 1
[[[]],[],[]]
=> [[.,[.,[.,.]]],.]
=> [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> 6
[[[]],[[]]]
=> [[.,[[.,.],.]],.]
=> [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> 1
[[[],[]],[]]
=> [[.,[.,.]],[.,.]]
=> [4,2,1,3] => ([(1,3),(2,3)],4)
=> 2
[[[[]]],[]]
=> [[[.,[.,.]],.],.]
=> [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> 2
[[[],[],[]]]
=> [[.,.],[.,[.,.]]]
=> [4,3,1,2] => ([(2,3)],4)
=> 2
[[[],[[]]]]
=> [[.,.],[[.,.],.]]
=> [3,4,1,2] => ([(0,3),(1,2)],4)
=> 2
[[[[]],[]]]
=> [[[.,.],.],[.,.]]
=> [4,1,2,3] => ([(1,2),(2,3)],4)
=> 1
[[[[],[]]]]
=> [[[.,.],[.,.]],.]
=> [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
=> 1
[[[[[]]]]]
=> [[[[.,.],.],.],.]
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1
[[],[],[],[],[]]
=> [.,[.,[.,[.,[.,.]]]]]
=> [5,4,3,2,1] => ([],5)
=> 120
[[],[],[],[[]]]
=> [.,[.,[.,[[.,.],.]]]]
=> [4,5,3,2,1] => ([(3,4)],5)
=> 6
[[],[],[[]],[]]
=> [.,[.,[[.,[.,.]],.]]]
=> [4,3,5,2,1] => ([(2,4),(3,4)],5)
=> 4
[[],[],[[],[]]]
=> [.,[.,[[.,.],[.,.]]]]
=> [5,3,4,2,1] => ([(3,4)],5)
=> 6
[[],[],[[[]]]]
=> [.,[.,[[[.,.],.],.]]]
=> [3,4,5,2,1] => ([(2,3),(3,4)],5)
=> 2
[[],[[]],[],[]]
=> [.,[[.,[.,[.,.]]],.]]
=> [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
=> 6
[[],[[]],[[]]]
=> [.,[[.,[[.,.],.]],.]]
=> [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
=> 1
[[],[[],[]],[]]
=> [.,[[.,[.,.]],[.,.]]]
=> [5,3,2,4,1] => ([(2,4),(3,4)],5)
=> 4
[[],[[[]]],[]]
=> [.,[[[.,[.,.]],.],.]]
=> [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
=> 2
[[],[[],[],[]]]
=> [.,[[.,.],[.,[.,.]]]]
=> [5,4,2,3,1] => ([(3,4)],5)
=> 6
[[],[[],[[]]]]
=> [.,[[.,.],[[.,.],.]]]
=> [4,5,2,3,1] => ([(1,4),(2,3)],5)
=> 2
[[],[[[]],[]]]
=> [.,[[[.,.],.],[.,.]]]
=> [5,2,3,4,1] => ([(2,3),(3,4)],5)
=> 2
[[],[[[],[]]]]
=> [.,[[[.,.],[.,.]],.]]
=> [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
=> 1
[[],[[[[]]]]]
=> [.,[[[[.,.],.],.],.]]
=> [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
=> 1
[[[]],[],[],[]]
=> [[.,[.,[.,[.,.]]]],.]
=> [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 24
[[[]],[],[[]]]
=> [[.,[.,[[.,.],.]]],.]
=> [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 2
[[[]],[[]],[]]
=> [[.,[[.,[.,.]],.]],.]
=> [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
=> 2
[[[]],[[],[]]]
=> [[.,.],[[.,.],[.,.]]]
=> [5,3,4,1,2] => ([(1,4),(2,3)],5)
=> 2
[[[]],[[[]]]]
=> [[.,[[[.,.],.],.]],.]
=> [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> 1
[[[],[]],[],[]]
=> [[.,[.,.]],[.,[.,.]]]
=> [5,4,2,1,3] => ([(2,4),(3,4)],5)
=> 4
[[[[]]],[],[]]
=> [[[.,[.,[.,.]]],.],.]
=> [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
=> 6
[[[],[]],[[]]]
=> [[.,[.,.]],[[.,.],.]]
=> [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
=> 2
[[[[]]],[[]]]
=> [[[.,[[.,.],.]],.],.]
=> [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
=> 1
[[[],[],[]],[]]
=> [[.,[.,[.,.]]],[.,.]]
=> [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5)
=> 6
[[[],[[]]],[]]
=> [[.,[[.,.],.]],[.,.]]
=> [5,2,3,1,4] => ([(1,4),(2,3),(3,4)],5)
=> 1
[[[[]],[]],[]]
=> [[[.,[.,.]],.],[.,.]]
=> [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5)
=> 2
[[[[],[]]],[]]
=> [[[.,[.,.]],[.,.]],.]
=> [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
=> 2
[[[[[]]]],[]]
=> [[[[.,[.,.]],.],.],.]
=> [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> 2
[[[],[],[],[]]]
=> [[.,.],[.,[.,[.,.]]]]
=> [5,4,3,1,2] => ([(3,4)],5)
=> 6
Description
The size of the automorphism group of a poset.
A poset automorphism is a permutation of the elements of the poset preserving the order relation.
Matching statistic: St001630
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(load all 3 compositions to match this statistic)
Values
[[],[]]
=> ([(0,2),(1,2)],3)
=> ([],1)
=> ? = 2
[[[]]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1
[[],[],[]]
=> ([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ? ∊ {1,1,1,6}
[[],[[]]]
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,6}
[[[]],[]]
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,6}
[[[],[]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ([],1)
=> ? ∊ {1,1,1,6}
[[[[]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[[],[],[],[]]
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[],[],[[]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[],[[]],[]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[],[[],[]]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[],[[[]]]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[[[]],[],[]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[[]],[[]]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[],[]],[]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[[[]]],[]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[[[],[],[]]]
=> ([(0,4),(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[[],[[]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[[[]],[]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[[[],[]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[[[[]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[[],[],[],[],[]]
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[],[[]]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[[]],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[[],[]]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[[[]]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 1
[[],[[]],[],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[]],[[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[],[[],[]],[]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[[]]],[]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 1
[[],[[],[],[]]]
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[],[[]]]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[[]],[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[[],[]]]]
=> ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[[[]]]]]
=> ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[[[]],[],[],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[]],[],[[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[]],[[]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[]],[[],[]]]
=> ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[]],[[[]]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[[[],[]],[],[]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]]],[],[]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 1
[[[],[]],[[]]]
=> ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]]],[[]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[[[],[],[]],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[]]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]],[]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[],[]]],[]]
=> ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[]]]],[]]
=> ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[[[],[],[],[]]]
=> ([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[],[[]]]]
=> ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[]],[]]]
=> ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[],[]]]]
=> ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[[]]]]]
=> ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 1
[[[[]],[],[]]]
=> ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]],[[]]]]
=> ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[[],[]],[]]]
=> ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[]]],[]]]
=> ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 1
[[[[],[],[]]]]
=> ([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[],[[]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[]],[]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[],[]]]]]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[[]]]]]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1
[[],[],[],[],[],[]]
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[],[],[],[],[[]]]
=> ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[],[],[],[[]],[]]
=> ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[],[],[],[[],[]]]
=> ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[],[],[],[[[]]]]
=> ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
[[],[],[[]],[],[]]
=> ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[],[],[[]],[[]]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[],[],[[],[]],[]]
=> ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[],[],[[[]]],[]]
=> ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
[[],[],[[],[],[]]]
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[],[],[[[[]]]]]
=> ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[[],[[]],[],[[]]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[],[[]],[[]],[]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[],[[]],[[[]]]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[[],[[[]]],[],[]]
=> ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
[[],[[[]]],[[]]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[[],[[[[]]]],[]]
=> ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[[],[[],[[[]]]]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
[[],[[[]],[[]]]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[],[[[[]]],[]]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
[[],[[[[[]]]]]]
=> ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[[[]],[],[],[[]]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[]],[],[[]],[]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[]],[],[[[]]]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[[[]],[[]],[],[]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[]],[[[]]],[]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[[[]],[[],[[]]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[]],[[[]],[]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[[]]],[],[],[]]
=> ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
[[[[]]],[],[[]]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[[[[]]],[[]],[]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[[[],[]],[[[]]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
[[[[]]],[[],[]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
[[[[[]]]],[],[]]
=> ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[[[],[[]]],[[]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[[]],[]],[[]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[],[[[]]]],[]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
Description
The global dimension of the incidence algebra of the lattice over the rational numbers.
Matching statistic: St001878
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
[[],[]]
=> ([(0,2),(1,2)],3)
=> ([],1)
=> ? = 2
[[[]]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1
[[],[],[]]
=> ([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ? ∊ {1,1,2,6}
[[],[[]]]
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,6}
[[[]],[]]
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,6}
[[[],[]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ([],1)
=> ? ∊ {1,1,2,6}
[[[[]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[[],[],[],[]]
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[],[],[[]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[],[[]],[]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[],[[],[]]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[],[[[]]]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[[[]],[],[]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[[]],[[]]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[],[]],[]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[[[]]],[]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[[[],[],[]]]
=> ([(0,4),(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[[],[[]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[[[]],[]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[[[],[]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,6,24}
[[[[[]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[[],[],[],[],[]]
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[],[[]]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[[]],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[[],[]]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[[[]]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 1
[[],[[]],[],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[]],[[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[],[[],[]],[]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[[]]],[]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 1
[[],[[],[],[]]]
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[],[[]]]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[[]],[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[[],[]]]]
=> ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[[[]]]]]
=> ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[[[]],[],[],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[]],[],[[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[]],[[]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[]],[[],[]]]
=> ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[]],[[[]]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[[[],[]],[],[]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]]],[],[]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 1
[[[],[]],[[]]]
=> ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]]],[[]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[[[],[],[]],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[]]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]],[]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[],[]]],[]]
=> ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[]]]],[]]
=> ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[[[],[],[],[]]]
=> ([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[],[[]]]]
=> ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[]],[]]]
=> ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[],[]]]]
=> ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[[]]]]]
=> ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 1
[[[[]],[],[]]]
=> ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]],[[]]]]
=> ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[[],[]],[]]]
=> ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[]]],[]]]
=> ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 1
[[[[],[],[]]]]
=> ([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[],[[]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[]],[]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[],[]]]]]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[[]]]]]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1
[[],[],[],[],[],[]]
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[],[],[],[],[[]]]
=> ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[],[],[],[[]],[]]
=> ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[],[],[],[[],[]]]
=> ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[],[],[],[[[]]]]
=> ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
[[],[],[[]],[],[]]
=> ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[],[],[[]],[[]]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[],[],[[],[]],[]]
=> ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[],[],[[[]]],[]]
=> ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
[[],[],[[],[],[]]]
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[],[],[[[[]]]]]
=> ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[[],[[]],[],[[]]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[],[[]],[[]],[]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[],[[]],[[[]]]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[[],[[[]]],[],[]]
=> ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
[[],[[[]]],[[]]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[[],[[[[]]]],[]]
=> ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[[],[[],[[[]]]]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
[[],[[[]],[[]]]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[],[[[[]]],[]]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
[[],[[[[[]]]]]]
=> ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[[[]],[],[],[[]]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[]],[],[[]],[]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[]],[],[[[]]]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[[[]],[[]],[],[]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[]],[[[]]],[]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[[[]],[[],[[]]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[]],[[[]],[]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[[]]],[],[],[]]
=> ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
[[[[]]],[],[[]]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[[[[]]],[[]],[]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[[[],[]],[[[]]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
[[[[]]],[[],[]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
[[[[[]]]],[],[]]
=> ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[[[],[[]]],[[]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[[]],[]],[[]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[[[],[[[]]]],[]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1
Description
The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.
Matching statistic: St000259
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00050: Ordered trees —to binary tree: right brother = right child⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 22% ●values known / values provided: 33%●distinct values known / distinct values provided: 22%
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 22% ●values known / values provided: 33%●distinct values known / distinct values provided: 22%
Values
[[],[]]
=> [.,[.,.]]
=> [2,1] => ([(0,1)],2)
=> 1
[[[]]]
=> [[.,.],.]
=> [1,2] => ([],2)
=> ? = 2
[[],[],[]]
=> [.,[.,[.,.]]]
=> [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
[[],[[]]]
=> [.,[[.,.],.]]
=> [2,3,1] => ([(0,2),(1,2)],3)
=> 2
[[[]],[]]
=> [[.,.],[.,.]]
=> [1,3,2] => ([(1,2)],3)
=> ? ∊ {1,1,6}
[[[],[]]]
=> [[.,[.,.]],.]
=> [2,1,3] => ([(1,2)],3)
=> ? ∊ {1,1,6}
[[[[]]]]
=> [[[.,.],.],.]
=> [1,2,3] => ([],3)
=> ? ∊ {1,1,6}
[[],[],[],[]]
=> [.,[.,[.,[.,.]]]]
=> [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[[],[],[[]]]
=> [.,[.,[[.,.],.]]]
=> [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[[],[[]],[]]
=> [.,[[.,.],[.,.]]]
=> [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[[],[[],[]]]
=> [.,[[.,[.,.]],.]]
=> [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[[],[[[]]]]
=> [.,[[[.,.],.],.]]
=> [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 2
[[[]],[],[]]
=> [[.,.],[.,[.,.]]]
=> [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,2,2,2,6,24}
[[[]],[[]]]
=> [[.,.],[[.,.],.]]
=> [1,3,4,2] => ([(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,2,2,2,6,24}
[[[],[]],[]]
=> [[.,[.,.]],[.,.]]
=> [2,1,4,3] => ([(0,3),(1,2)],4)
=> ? ∊ {1,1,1,1,2,2,2,6,24}
[[[[]]],[]]
=> [[[.,.],.],[.,.]]
=> [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {1,1,1,1,2,2,2,6,24}
[[[],[],[]]]
=> [[.,[.,[.,.]]],.]
=> [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,2,2,2,6,24}
[[[],[[]]]]
=> [[.,[[.,.],.]],.]
=> [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,2,2,2,6,24}
[[[[]],[]]]
=> [[[.,.],[.,.]],.]
=> [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {1,1,1,1,2,2,2,6,24}
[[[[],[]]]]
=> [[[.,[.,.]],.],.]
=> [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {1,1,1,1,2,2,2,6,24}
[[[[[]]]]]
=> [[[[.,.],.],.],.]
=> [1,2,3,4] => ([],4)
=> ? ∊ {1,1,1,1,2,2,2,6,24}
[[],[],[],[],[]]
=> [.,[.,[.,[.,[.,.]]]]]
=> [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[[],[],[],[[]]]
=> [.,[.,[.,[[.,.],.]]]]
=> [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[[],[],[[]],[]]
=> [.,[.,[[.,.],[.,.]]]]
=> [3,5,4,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[[],[],[[],[]]]
=> [.,[.,[[.,[.,.]],.]]]
=> [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[[],[],[[[]]]]
=> [.,[.,[[[.,.],.],.]]]
=> [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[[],[[]],[],[]]
=> [.,[[.,.],[.,[.,.]]]]
=> [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[[],[[]],[[]]]
=> [.,[[.,.],[[.,.],.]]]
=> [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[[],[[],[]],[]]
=> [.,[[.,[.,.]],[.,.]]]
=> [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
[[],[[[]]],[]]
=> [.,[[[.,.],.],[.,.]]]
=> [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[[],[[],[],[]]]
=> [.,[[.,[.,[.,.]]],.]]
=> [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[[],[[],[[]]]]
=> [.,[[.,[[.,.],.]],.]]
=> [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[[],[[[]],[]]]
=> [.,[[[.,.],[.,.]],.]]
=> [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[[],[[[],[]]]]
=> [.,[[[.,[.,.]],.],.]]
=> [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[[],[[[[]]]]]
=> [.,[[[[.,.],.],.],.]]
=> [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
[[[]],[],[],[]]
=> [[.,.],[.,[.,[.,.]]]]
=> [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[]],[],[[]]]
=> [[.,.],[.,[[.,.],.]]]
=> [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[]],[[]],[]]
=> [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[]],[[],[]]]
=> [[.,.],[[.,[.,.]],.]]
=> [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[]],[[[]]]]
=> [[.,.],[[[.,.],.],.]]
=> [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[]],[],[]]
=> [[.,[.,.]],[.,[.,.]]]
=> [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]]],[],[]]
=> [[[.,.],.],[.,[.,.]]]
=> [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[]],[[]]]
=> [[.,[.,.]],[[.,.],.]]
=> [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]]],[[]]]
=> [[[.,.],.],[[.,.],.]]
=> [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[],[]],[]]
=> [[.,[.,[.,.]]],[.,.]]
=> [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[]]],[]]
=> [[.,[[.,.],.]],[.,.]]
=> [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]],[]],[]]
=> [[[.,.],[.,.]],[.,.]]
=> [1,3,2,5,4] => ([(1,4),(2,3)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[],[]]],[]]
=> [[[.,[.,.]],.],[.,.]]
=> [2,1,3,5,4] => ([(1,4),(2,3)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[]]]],[]]
=> [[[[.,.],.],.],[.,.]]
=> [1,2,3,5,4] => ([(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[],[],[]]]
=> [[.,[.,[.,[.,.]]]],.]
=> [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[],[[]]]]
=> [[.,[.,[[.,.],.]]],.]
=> [3,4,2,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[]],[]]]
=> [[.,[[.,.],[.,.]]],.]
=> [2,4,3,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[],[]]]]
=> [[.,[[.,[.,.]],.]],.]
=> [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[[]]]]]
=> [[.,[[[.,.],.],.]],.]
=> [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]],[],[]]]
=> [[[.,.],[.,[.,.]]],.]
=> [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]],[[]]]]
=> [[[.,.],[[.,.],.]],.]
=> [1,3,4,2,5] => ([(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[],[]],[]]]
=> [[[.,[.,.]],[.,.]],.]
=> [2,1,4,3,5] => ([(1,4),(2,3)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[]]],[]]]
=> [[[[.,.],.],[.,.]],.]
=> [1,2,4,3,5] => ([(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[],[],[]]]]
=> [[[.,[.,[.,.]]],.],.]
=> [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[],[[]]]]]
=> [[[.,[[.,.],.]],.],.]
=> [2,3,1,4,5] => ([(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[]],[]]]]
=> [[[[.,.],[.,.]],.],.]
=> [1,3,2,4,5] => ([(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[],[]]]]]
=> [[[[.,[.,.]],.],.],.]
=> [2,1,3,4,5] => ([(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[[]]]]]]
=> [[[[[.,.],.],.],.],.]
=> [1,2,3,4,5] => ([],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[],[],[],[]]
=> [.,[.,[.,[.,[.,[.,.]]]]]]
=> [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
[[],[],[],[],[[]]]
=> [.,[.,[.,[.,[[.,.],.]]]]]
=> [5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[],[],[[]],[]]
=> [.,[.,[.,[[.,.],[.,.]]]]]
=> [4,6,5,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[],[],[[],[]]]
=> [.,[.,[.,[[.,[.,.]],.]]]]
=> [5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[],[],[[[]]]]
=> [.,[.,[.,[[[.,.],.],.]]]]
=> [4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[],[[]],[],[]]
=> [.,[.,[[.,.],[.,[.,.]]]]]
=> [3,6,5,4,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[],[[]],[[]]]
=> [.,[.,[[.,.],[[.,.],.]]]]
=> [3,5,6,4,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[],[[],[]],[]]
=> [.,[.,[[.,[.,.]],[.,.]]]]
=> [4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[],[[[]]],[]]
=> [.,[.,[[[.,.],.],[.,.]]]]
=> [3,4,6,5,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[],[[],[],[]]]
=> [.,[.,[[.,[.,[.,.]]],.]]]
=> [5,4,3,6,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[],[[],[[]]]]
=> [.,[.,[[.,[[.,.],.]],.]]]
=> [4,5,3,6,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[],[[[]],[]]]
=> [.,[.,[[[.,.],[.,.]],.]]]
=> [3,5,4,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[],[[[],[]]]]
=> [.,[.,[[[.,[.,.]],.],.]]]
=> [4,3,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[],[[[[]]]]]
=> [.,[.,[[[[.,.],.],.],.]]]
=> [3,4,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[[]],[],[],[]]
=> [.,[[.,.],[.,[.,[.,.]]]]]
=> [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[[]],[],[[]]]
=> [.,[[.,.],[.,[[.,.],.]]]]
=> [2,5,6,4,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[[]],[[]],[]]
=> [.,[[.,.],[[.,.],[.,.]]]]
=> [2,4,6,5,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[[]],[[],[]]]
=> [.,[[.,.],[[.,[.,.]],.]]]
=> [2,5,4,6,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[[]],[[[]]]]
=> [.,[[.,.],[[[.,.],.],.]]]
=> [2,4,5,6,3,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[[],[]],[],[]]
=> [.,[[.,[.,.]],[.,[.,.]]]]
=> [3,2,6,5,4,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[[[]]],[],[]]
=> [.,[[[.,.],.],[.,[.,.]]]]
=> [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[[],[]],[[]]]
=> [.,[[.,[.,.]],[[.,.],.]]]
=> [3,2,5,6,4,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[[[]]],[[]]]
=> [.,[[[.,.],.],[[.,.],.]]]
=> [2,3,5,6,4,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[[],[],[]],[]]
=> [.,[[.,[.,[.,.]]],[.,.]]]
=> [4,3,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[[],[[]]],[]]
=> [.,[[.,[[.,.],.]],[.,.]]]
=> [3,4,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[],[[[]],[]],[]]
=> [.,[[[.,.],[.,.]],[.,.]]]
=> [2,4,3,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> 2
[[],[[[],[]]],[]]
=> [.,[[[.,[.,.]],.],[.,.]]]
=> [3,2,4,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> 2
[[],[[[[]]]],[]]
=> [.,[[[[.,.],.],.],[.,.]]]
=> [2,3,4,6,5,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[[[]],[],[],[],[]]
=> [[.,.],[.,[.,[.,[.,.]]]]]
=> [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[[]],[],[],[[]]]
=> [[.,.],[.,[.,[[.,.],.]]]]
=> [1,5,6,4,3,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[[]],[],[[]],[]]
=> [[.,.],[.,[[.,.],[.,.]]]]
=> [1,4,6,5,3,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[[]],[],[[],[]]]
=> [[.,.],[.,[[.,[.,.]],.]]]
=> [1,5,4,6,3,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[[]],[],[[[]]]]
=> [[.,.],[.,[[[.,.],.],.]]]
=> [1,4,5,6,3,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[[]],[[]],[],[]]
=> [[.,.],[[.,.],[.,[.,.]]]]
=> [1,3,6,5,4,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[[]],[[]],[[]]]
=> [[.,.],[[.,.],[[.,.],.]]]
=> [1,3,5,6,4,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[[]],[[],[]],[]]
=> [[.,.],[[.,[.,.]],[.,.]]]
=> [1,4,3,6,5,2] => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
[[[]],[[[]]],[]]
=> [[.,.],[[[.,.],.],[.,.]]]
=> [1,3,4,6,5,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,12,12,12,12,12,12,12,24,24,24,24,24,24,24,24,120,720}
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
Matching statistic: St000260
Values
[[],[]]
=> ([(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,2}
[[[]]]
=> ([(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {1,2}
[[],[],[]]
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {1,1,1,2,6}
[[],[[]]]
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> ? ∊ {1,1,1,2,6}
[[[]],[]]
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> ? ∊ {1,1,1,2,6}
[[[],[]]]
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {1,1,1,2,6}
[[[[]]]]
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> ? ∊ {1,1,1,2,6}
[[],[],[],[]]
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,6,24}
[[],[],[[]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,6,24}
[[],[[]],[]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,6,24}
[[],[[],[]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,6,24}
[[],[[[]]]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,6,24}
[[[]],[],[]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,6,24}
[[[]],[[]]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,6,24}
[[[],[]],[]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,6,24}
[[[[]]],[]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,6,24}
[[[],[],[]]]
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,6,24}
[[[],[[]]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,6,24}
[[[[]],[]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,6,24}
[[[[],[]]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,6,24}
[[[[[]]]]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,6,24}
[[],[],[],[],[]]
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[],[[]]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[[]],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[[],[]]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[[[]]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[]],[],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[]],[[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[],[]],[]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[[]]],[]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[],[],[]]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[],[[]]]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[[]],[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[[],[]]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[[[]]]]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 2
[[[]],[],[],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[]],[],[[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[]],[[]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[]],[[],[]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[]],[[[]]]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 2
[[[],[]],[],[]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]]],[],[]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[]],[[]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]]],[[]]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 2
[[[],[],[]],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[]]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]],[]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[],[]]],[]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[]]]],[]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 2
[[[],[],[],[]]]
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[],[[]]]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[]],[]]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[],[]]]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[[]]]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[[]]]]]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 2
[[],[],[[[[]]]]]
=> ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[[],[[]],[[[]]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[],[[[]]],[[]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[],[[[[]]]],[]]
=> ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[[],[[],[[[]]]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[],[[[[]]],[]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[],[[[],[[]]]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[],[[[[]],[]]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[],[[[[],[]]]]]
=> ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[[],[[[[[]]]]]]
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
=> 2
[[[]],[],[[[]]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[]],[[[]]],[]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[]],[[],[[]]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[]],[[[]],[]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[]],[[[],[]]]]
=> ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[[[]],[[[[]]]]]
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
=> 2
[[[[]]],[],[[]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[[]]],[[]],[]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[],[]],[[[]]]]
=> ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[[[[]]],[[],[]]]
=> ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[[[[]]],[[[]]]]
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
=> 2
[[[[[]]]],[],[]]
=> ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[[[],[[]]],[[]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[[]],[]],[[]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[[],[]]],[[]]]
=> ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[[[[[]]]],[[]]]
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
=> 2
[[[],[[[]]]],[]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[[[]]],[]],[]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[[],[[]]]],[]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[[[]],[]]],[]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[[[],[]]]],[]]
=> ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[[[[[[]]]]],[]]
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
=> 2
[[[],[[[[]]]]]]
=> ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[[[[]],[[[]]]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[[[]]],[[]]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[[[[]]]],[]]]
=> ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[[[[],[[[]]]]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[[[[]]],[]]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[[[],[[]]]]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[[[[]],[]]]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
=> 2
[[[[[[],[]]]]]]
=> ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[[[[[[[]]]]]]]
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
=> 2
Description
The radius of a connected graph.
This is the minimum eccentricity of any vertex.
Matching statistic: St001877
Values
[[],[]]
=> ([(0,2),(1,2)],3)
=> ([],1)
=> ([],1)
=> ? = 2
[[[]]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[],[],[]]
=> ([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,2,6}
[[],[[]]]
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,2,6}
[[[]],[]]
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,2,6}
[[[],[]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,2,6}
[[[[]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(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)
=> ? ∊ {1,1,1,2,6}
[[],[],[],[]]
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,6,24}
[[],[],[[]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,6,24}
[[],[[]],[]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,6,24}
[[],[[],[]]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,6,24}
[[],[[[]]]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[]],[],[]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,6,24}
[[[]],[[]]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[],[]],[]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,6,24}
[[[[]]],[]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[],[],[]]]
=> ([(0,4),(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,6,24}
[[[],[[]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,6,24}
[[[[]],[]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,6,24}
[[[[],[]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,6,24}
[[[[[]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? ∊ {1,1,2,2,2,2,2,2,2,6,24}
[[],[],[],[],[]]
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[],[[]]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[[]],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[[],[]]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[[[]]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[],[[]],[],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[]],[[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[],[[],[]],[]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[[]]],[]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[],[[],[],[]]]
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[],[[]]]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[[]],[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[[],[]]]]
=> ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[[[[]]]]]
=> ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(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)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[]],[],[],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[]],[],[[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[]],[[]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[]],[[],[]]]
=> ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[]],[[[]]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],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)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[]],[],[]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]]],[],[]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[],[]],[[]]]
=> ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]]],[[]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],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)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[],[]],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[]]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]],[]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[],[]]],[]]
=> ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[]]]],[]]
=> ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(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)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[],[],[]]]
=> ([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[],[[]]]]
=> ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[]],[]]]
=> ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[],[]]]]
=> ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[],[[[]]]]]
=> ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[[]],[],[]]]
=> ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[]],[[]]]]
=> ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[[],[]],[]]]
=> ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[]]],[]]]
=> ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[[],[],[]]]]
=> ([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[],[[]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[]],[]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[],[]]]]]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[[[[[]]]]]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,24,120}
[[],[],[],[[[]]]]
=> ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[],[],[[]],[[]]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[],[],[[[]]],[]]
=> ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[],[[]],[],[[]]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[],[[]],[[]],[]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[],[[[]]],[],[]]
=> ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[],[[],[[[]]]]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[],[[[]],[[]]]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[],[[[[]]],[]]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[]],[],[],[[]]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[]],[],[[]],[]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[]],[[]],[],[]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[]],[[],[[]]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[]],[[[]],[]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[[]]],[],[],[]]
=> ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[],[]],[[[]]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[[]]],[[],[]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[],[[]]],[[]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[[]],[]],[[]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[],[[[]]]],[]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[[]],[[]]],[]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[[[]]],[]],[]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[],[],[[[]]]]]
=> ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[],[[]],[[]]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[],[[[]]],[]]]
=> ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[[]],[],[[]]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[[]],[[]],[]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[[[]]],[],[]]]
=> ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[[],[[[]]]]]]
=> ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[[[]],[[]]]]]
=> ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[[[[[]]],[]]]]
=> ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
=> ([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
Description
Number of indecomposable injective modules with projective dimension 2.
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