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Your data matches 16 different statistics following compositions of up to 3 maps.
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Matching statistic: St000308
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(load all 3 compositions to match this statistic)
Mp00049: Ordered trees —to binary tree: left brother = left child⟶ Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
St000308: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
St000308: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[]]
=> [.,.]
=> [1] => 1
[[],[]]
=> [[.,.],.]
=> [1,2] => 2
[[[]]]
=> [.,[.,.]]
=> [2,1] => 1
[[],[],[]]
=> [[[.,.],.],.]
=> [1,2,3] => 3
[[],[[]]]
=> [[.,.],[.,.]]
=> [3,1,2] => 2
[[[]],[]]
=> [[.,[.,.]],.]
=> [2,1,3] => 2
[[[],[]]]
=> [.,[[.,.],.]]
=> [2,3,1] => 2
[[[[]]]]
=> [.,[.,[.,.]]]
=> [3,2,1] => 1
[[],[],[],[]]
=> [[[[.,.],.],.],.]
=> [1,2,3,4] => 4
[[],[],[[]]]
=> [[[.,.],.],[.,.]]
=> [4,1,2,3] => 3
[[],[[]],[]]
=> [[[.,.],[.,.]],.]
=> [3,1,2,4] => 3
[[],[[],[]]]
=> [[.,.],[[.,.],.]]
=> [3,4,1,2] => 2
[[],[[[]]]]
=> [[.,.],[.,[.,.]]]
=> [4,3,1,2] => 2
[[[]],[],[]]
=> [[[.,[.,.]],.],.]
=> [2,1,3,4] => 3
[[[]],[[]]]
=> [[.,[.,.]],[.,.]]
=> [4,2,1,3] => 2
[[[],[]],[]]
=> [[.,[[.,.],.]],.]
=> [2,3,1,4] => 2
[[[[]]],[]]
=> [[.,[.,[.,.]]],.]
=> [3,2,1,4] => 2
[[[],[],[]]]
=> [.,[[[.,.],.],.]]
=> [2,3,4,1] => 3
[[[],[[]]]]
=> [.,[[.,.],[.,.]]]
=> [4,2,3,1] => 2
[[[[]],[]]]
=> [.,[[.,[.,.]],.]]
=> [3,2,4,1] => 2
[[[[],[]]]]
=> [.,[.,[[.,.],.]]]
=> [3,4,2,1] => 2
[[[[[]]]]]
=> [.,[.,[.,[.,.]]]]
=> [4,3,2,1] => 1
[[],[],[],[],[]]
=> [[[[[.,.],.],.],.],.]
=> [1,2,3,4,5] => 5
[[],[],[],[[]]]
=> [[[[.,.],.],.],[.,.]]
=> [5,1,2,3,4] => 4
[[],[],[[]],[]]
=> [[[[.,.],.],[.,.]],.]
=> [4,1,2,3,5] => 4
[[],[],[[],[]]]
=> [[[.,.],.],[[.,.],.]]
=> [4,5,1,2,3] => 3
[[],[],[[[]]]]
=> [[[.,.],.],[.,[.,.]]]
=> [5,4,1,2,3] => 3
[[],[[]],[],[]]
=> [[[[.,.],[.,.]],.],.]
=> [3,1,2,4,5] => 4
[[],[[]],[[]]]
=> [[[.,.],[.,.]],[.,.]]
=> [5,3,1,2,4] => 3
[[],[[],[]],[]]
=> [[[.,.],[[.,.],.]],.]
=> [3,4,1,2,5] => 3
[[],[[[]]],[]]
=> [[[.,.],[.,[.,.]]],.]
=> [4,3,1,2,5] => 3
[[],[[],[],[]]]
=> [[.,.],[[[.,.],.],.]]
=> [3,4,5,1,2] => 3
[[],[[],[[]]]]
=> [[.,.],[[.,.],[.,.]]]
=> [5,3,4,1,2] => 2
[[],[[[]],[]]]
=> [[.,.],[[.,[.,.]],.]]
=> [4,3,5,1,2] => 2
[[],[[[],[]]]]
=> [[.,.],[.,[[.,.],.]]]
=> [4,5,3,1,2] => 2
[[],[[[[]]]]]
=> [[.,.],[.,[.,[.,.]]]]
=> [5,4,3,1,2] => 2
[[[]],[],[],[]]
=> [[[[.,[.,.]],.],.],.]
=> [2,1,3,4,5] => 4
[[[]],[],[[]]]
=> [[[.,[.,.]],.],[.,.]]
=> [5,2,1,3,4] => 3
[[[]],[[]],[]]
=> [[[.,[.,.]],[.,.]],.]
=> [4,2,1,3,5] => 3
[[[]],[[],[]]]
=> [[.,[.,.]],[[.,.],.]]
=> [4,5,2,1,3] => 2
[[[]],[[[]]]]
=> [[.,[.,.]],[.,[.,.]]]
=> [5,4,2,1,3] => 2
[[[],[]],[],[]]
=> [[[.,[[.,.],.]],.],.]
=> [2,3,1,4,5] => 3
[[[[]]],[],[]]
=> [[[.,[.,[.,.]]],.],.]
=> [3,2,1,4,5] => 3
[[[],[]],[[]]]
=> [[.,[[.,.],.]],[.,.]]
=> [5,2,3,1,4] => 2
[[[[]]],[[]]]
=> [[.,[.,[.,.]]],[.,.]]
=> [5,3,2,1,4] => 2
[[[],[],[]],[]]
=> [[.,[[[.,.],.],.]],.]
=> [2,3,4,1,5] => 3
[[[],[[]]],[]]
=> [[.,[[.,.],[.,.]]],.]
=> [4,2,3,1,5] => 2
[[[[]],[]],[]]
=> [[.,[[.,[.,.]],.]],.]
=> [3,2,4,1,5] => 2
[[[[],[]]],[]]
=> [[.,[.,[[.,.],.]]],.]
=> [3,4,2,1,5] => 2
[[[[[]]]],[]]
=> [[.,[.,[.,[.,.]]]],.]
=> [4,3,2,1,5] => 2
Description
The height of the tree associated to a permutation.
A permutation can be mapped to a rooted tree with vertices $\{0,1,2,\ldots,n\}$ and root $0$ in the following way. Entries of the permutations are inserted one after the other, each child is larger than its parent and the children are in strict order from left to right. Details of the construction are found in [1].
The statistic is given by the height of this tree.
See also [[St000325]] for the width of this tree.
Matching statistic: St000381
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00049: Ordered trees —to binary tree: left brother = left child⟶ Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
St000381: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
St000381: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[]]
=> [.,.]
=> [1,0]
=> [1] => 1
[[],[]]
=> [[.,.],.]
=> [1,1,0,0]
=> [2] => 2
[[[]]]
=> [.,[.,.]]
=> [1,0,1,0]
=> [1,1] => 1
[[],[],[]]
=> [[[.,.],.],.]
=> [1,1,1,0,0,0]
=> [3] => 3
[[],[[]]]
=> [[.,.],[.,.]]
=> [1,1,0,0,1,0]
=> [2,1] => 2
[[[]],[]]
=> [[.,[.,.]],.]
=> [1,1,0,1,0,0]
=> [2,1] => 2
[[[],[]]]
=> [.,[[.,.],.]]
=> [1,0,1,1,0,0]
=> [1,2] => 2
[[[[]]]]
=> [.,[.,[.,.]]]
=> [1,0,1,0,1,0]
=> [1,1,1] => 1
[[],[],[],[]]
=> [[[[.,.],.],.],.]
=> [1,1,1,1,0,0,0,0]
=> [4] => 4
[[],[],[[]]]
=> [[[.,.],.],[.,.]]
=> [1,1,1,0,0,0,1,0]
=> [3,1] => 3
[[],[[]],[]]
=> [[[.,.],[.,.]],.]
=> [1,1,1,0,0,1,0,0]
=> [3,1] => 3
[[],[[],[]]]
=> [[.,.],[[.,.],.]]
=> [1,1,0,0,1,1,0,0]
=> [2,2] => 2
[[],[[[]]]]
=> [[.,.],[.,[.,.]]]
=> [1,1,0,0,1,0,1,0]
=> [2,1,1] => 2
[[[]],[],[]]
=> [[[.,[.,.]],.],.]
=> [1,1,1,0,1,0,0,0]
=> [3,1] => 3
[[[]],[[]]]
=> [[.,[.,.]],[.,.]]
=> [1,1,0,1,0,0,1,0]
=> [2,1,1] => 2
[[[],[]],[]]
=> [[.,[[.,.],.]],.]
=> [1,1,0,1,1,0,0,0]
=> [2,2] => 2
[[[[]]],[]]
=> [[.,[.,[.,.]]],.]
=> [1,1,0,1,0,1,0,0]
=> [2,1,1] => 2
[[[],[],[]]]
=> [.,[[[.,.],.],.]]
=> [1,0,1,1,1,0,0,0]
=> [1,3] => 3
[[[],[[]]]]
=> [.,[[.,.],[.,.]]]
=> [1,0,1,1,0,0,1,0]
=> [1,2,1] => 2
[[[[]],[]]]
=> [.,[[.,[.,.]],.]]
=> [1,0,1,1,0,1,0,0]
=> [1,2,1] => 2
[[[[],[]]]]
=> [.,[.,[[.,.],.]]]
=> [1,0,1,0,1,1,0,0]
=> [1,1,2] => 2
[[[[[]]]]]
=> [.,[.,[.,[.,.]]]]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1] => 1
[[],[],[],[],[]]
=> [[[[[.,.],.],.],.],.]
=> [1,1,1,1,1,0,0,0,0,0]
=> [5] => 5
[[],[],[],[[]]]
=> [[[[.,.],.],.],[.,.]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [4,1] => 4
[[],[],[[]],[]]
=> [[[[.,.],.],[.,.]],.]
=> [1,1,1,1,0,0,0,1,0,0]
=> [4,1] => 4
[[],[],[[],[]]]
=> [[[.,.],.],[[.,.],.]]
=> [1,1,1,0,0,0,1,1,0,0]
=> [3,2] => 3
[[],[],[[[]]]]
=> [[[.,.],.],[.,[.,.]]]
=> [1,1,1,0,0,0,1,0,1,0]
=> [3,1,1] => 3
[[],[[]],[],[]]
=> [[[[.,.],[.,.]],.],.]
=> [1,1,1,1,0,0,1,0,0,0]
=> [4,1] => 4
[[],[[]],[[]]]
=> [[[.,.],[.,.]],[.,.]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [3,1,1] => 3
[[],[[],[]],[]]
=> [[[.,.],[[.,.],.]],.]
=> [1,1,1,0,0,1,1,0,0,0]
=> [3,2] => 3
[[],[[[]]],[]]
=> [[[.,.],[.,[.,.]]],.]
=> [1,1,1,0,0,1,0,1,0,0]
=> [3,1,1] => 3
[[],[[],[],[]]]
=> [[.,.],[[[.,.],.],.]]
=> [1,1,0,0,1,1,1,0,0,0]
=> [2,3] => 3
[[],[[],[[]]]]
=> [[.,.],[[.,.],[.,.]]]
=> [1,1,0,0,1,1,0,0,1,0]
=> [2,2,1] => 2
[[],[[[]],[]]]
=> [[.,.],[[.,[.,.]],.]]
=> [1,1,0,0,1,1,0,1,0,0]
=> [2,2,1] => 2
[[],[[[],[]]]]
=> [[.,.],[.,[[.,.],.]]]
=> [1,1,0,0,1,0,1,1,0,0]
=> [2,1,2] => 2
[[],[[[[]]]]]
=> [[.,.],[.,[.,[.,.]]]]
=> [1,1,0,0,1,0,1,0,1,0]
=> [2,1,1,1] => 2
[[[]],[],[],[]]
=> [[[[.,[.,.]],.],.],.]
=> [1,1,1,1,0,1,0,0,0,0]
=> [4,1] => 4
[[[]],[],[[]]]
=> [[[.,[.,.]],.],[.,.]]
=> [1,1,1,0,1,0,0,0,1,0]
=> [3,1,1] => 3
[[[]],[[]],[]]
=> [[[.,[.,.]],[.,.]],.]
=> [1,1,1,0,1,0,0,1,0,0]
=> [3,1,1] => 3
[[[]],[[],[]]]
=> [[.,[.,.]],[[.,.],.]]
=> [1,1,0,1,0,0,1,1,0,0]
=> [2,1,2] => 2
[[[]],[[[]]]]
=> [[.,[.,.]],[.,[.,.]]]
=> [1,1,0,1,0,0,1,0,1,0]
=> [2,1,1,1] => 2
[[[],[]],[],[]]
=> [[[.,[[.,.],.]],.],.]
=> [1,1,1,0,1,1,0,0,0,0]
=> [3,2] => 3
[[[[]]],[],[]]
=> [[[.,[.,[.,.]]],.],.]
=> [1,1,1,0,1,0,1,0,0,0]
=> [3,1,1] => 3
[[[],[]],[[]]]
=> [[.,[[.,.],.]],[.,.]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [2,2,1] => 2
[[[[]]],[[]]]
=> [[.,[.,[.,.]]],[.,.]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [2,1,1,1] => 2
[[[],[],[]],[]]
=> [[.,[[[.,.],.],.]],.]
=> [1,1,0,1,1,1,0,0,0,0]
=> [2,3] => 3
[[[],[[]]],[]]
=> [[.,[[.,.],[.,.]]],.]
=> [1,1,0,1,1,0,0,1,0,0]
=> [2,2,1] => 2
[[[[]],[]],[]]
=> [[.,[[.,[.,.]],.]],.]
=> [1,1,0,1,1,0,1,0,0,0]
=> [2,2,1] => 2
[[[[],[]]],[]]
=> [[.,[.,[[.,.],.]]],.]
=> [1,1,0,1,0,1,1,0,0,0]
=> [2,1,2] => 2
[[[[[]]]],[]]
=> [[.,[.,[.,[.,.]]]],.]
=> [1,1,0,1,0,1,0,1,0,0]
=> [2,1,1,1] => 2
Description
The largest part of an integer composition.
Matching statistic: St000444
(load all 9 compositions to match this statistic)
(load all 9 compositions to match this statistic)
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St000444: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St000444: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[]]
=> [1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> 1
[[],[]]
=> [1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,0,1,1,0,0]
=> 2
[[[]]]
=> [1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 1
[[],[],[]]
=> [1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0]
=> 3
[[],[[]]]
=> [1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0]
=> 2
[[[]],[]]
=> [1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> 2
[[[],[]]]
=> [1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> 2
[[[[]]]]
=> [1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> 1
[[],[],[],[]]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 4
[[],[],[[]]]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> 3
[[],[[]],[]]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3
[[],[[],[]]]
=> [1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> 2
[[],[[[]]]]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> 2
[[[]],[],[]]
=> [1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> 3
[[[]],[[]]]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> 2
[[[],[]],[]]
=> [1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 2
[[[[]]],[]]
=> [1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> 2
[[[],[],[]]]
=> [1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3
[[[],[[]]]]
=> [1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> 2
[[[[]],[]]]
=> [1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> 2
[[[[],[]]]]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> 2
[[[[[]]]]]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> 1
[[],[],[],[],[]]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5
[[],[],[],[[]]]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> 4
[[],[],[[]],[]]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> 4
[[],[],[[],[]]]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> 3
[[],[],[[[]]]]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> 3
[[],[[]],[],[]]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> 4
[[],[[]],[[]]]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> 3
[[],[[],[]],[]]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> 3
[[],[[[]]],[]]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> 3
[[],[[],[],[]]]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> 3
[[],[[],[[]]]]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> 2
[[],[[[]],[]]]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> 2
[[],[[[],[]]]]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> 2
[[],[[[[]]]]]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> 2
[[[]],[],[],[]]
=> [1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> 4
[[[]],[],[[]]]
=> [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> 3
[[[]],[[]],[]]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> 3
[[[]],[[],[]]]
=> [1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> 2
[[[]],[[[]]]]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> 2
[[[],[]],[],[]]
=> [1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 3
[[[[]]],[],[]]
=> [1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> 3
[[[],[]],[[]]]
=> [1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> 2
[[[[]]],[[]]]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> 2
[[[],[],[]],[]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> 3
[[[],[[]]],[]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> 2
[[[[]],[]],[]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 2
[[[[],[]]],[]]
=> [1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> 2
[[[[[]]]],[]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> 2
Description
The length of the maximal rise of a Dyck path.
Matching statistic: St001062
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
St001062: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00030: Dyck paths —zeta map⟶ Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
St001062: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[]]
=> [1,0]
=> [1,0]
=> {{1}}
=> ? = 1
[[],[]]
=> [1,0,1,0]
=> [1,1,0,0]
=> {{1,2}}
=> 2
[[[]]]
=> [1,1,0,0]
=> [1,0,1,0]
=> {{1},{2}}
=> 1
[[],[],[]]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> {{1,2,3}}
=> 3
[[],[[]]]
=> [1,0,1,1,0,0]
=> [1,0,1,1,0,0]
=> {{1},{2,3}}
=> 2
[[[]],[]]
=> [1,1,0,0,1,0]
=> [1,1,0,1,0,0]
=> {{1,3},{2}}
=> 2
[[[],[]]]
=> [1,1,0,1,0,0]
=> [1,1,0,0,1,0]
=> {{1,2},{3}}
=> 2
[[[[]]]]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> {{1},{2},{3}}
=> 1
[[],[],[],[]]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> {{1,2,3,4}}
=> 4
[[],[],[[]]]
=> [1,0,1,0,1,1,0,0]
=> [1,0,1,1,1,0,0,0]
=> {{1},{2,3,4}}
=> 3
[[],[[]],[]]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,0]
=> {{1,3,4},{2}}
=> 3
[[],[[],[]]]
=> [1,0,1,1,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> {{1,2},{3,4}}
=> 2
[[],[[[]]]]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> {{1},{2},{3,4}}
=> 2
[[[]],[],[]]
=> [1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,0]
=> {{1,2,4},{3}}
=> 3
[[[]],[[]]]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,1,0,0]
=> {{1,4},{2},{3}}
=> 2
[[[],[]],[]]
=> [1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> {{1,4},{2,3}}
=> 2
[[[[]]],[]]
=> [1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,0,0]
=> {{1},{2,4},{3}}
=> 2
[[[],[],[]]]
=> [1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> {{1,2,3},{4}}
=> 3
[[[],[[]]]]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> {{1},{2,3},{4}}
=> 2
[[[[]],[]]]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> {{1,3},{2},{4}}
=> 2
[[[[],[]]]]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> {{1,2},{3},{4}}
=> 2
[[[[[]]]]]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> {{1},{2},{3},{4}}
=> 1
[[],[],[],[],[]]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> {{1,2,3,4,5}}
=> 5
[[],[],[],[[]]]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> {{1},{2,3,4,5}}
=> 4
[[],[],[[]],[]]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> {{1,3,4,5},{2}}
=> 4
[[],[],[[],[]]]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> {{1,2},{3,4,5}}
=> 3
[[],[],[[[]]]]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> {{1},{2},{3,4,5}}
=> 3
[[],[[]],[],[]]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> {{1,2,4,5},{3}}
=> 4
[[],[[]],[[]]]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> {{1,4,5},{2},{3}}
=> 3
[[],[[],[]],[]]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> {{1,4,5},{2,3}}
=> 3
[[],[[[]]],[]]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> {{1},{2,4,5},{3}}
=> 3
[[],[[],[],[]]]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> {{1,2,3},{4,5}}
=> 3
[[],[[],[[]]]]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> {{1},{2,3},{4,5}}
=> 2
[[],[[[]],[]]]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> {{1,3},{2},{4,5}}
=> 2
[[],[[[],[]]]]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> {{1,2},{3},{4,5}}
=> 2
[[],[[[[]]]]]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> {{1},{2},{3},{4,5}}
=> 2
[[[]],[],[],[]]
=> [1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> {{1,2,3,5},{4}}
=> 4
[[[]],[],[[]]]
=> [1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> {{1,3,5},{2},{4}}
=> 3
[[[]],[[]],[]]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> {{1,2,5},{3},{4}}
=> 3
[[[]],[[],[]]]
=> [1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> {{1,5},{2,3},{4}}
=> 2
[[[]],[[[]]]]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> {{1},{2,5},{3},{4}}
=> 2
[[[],[]],[],[]]
=> [1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> {{1,2,5},{3,4}}
=> 3
[[[[]]],[],[]]
=> [1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> {{1},{2,3,5},{4}}
=> 3
[[[],[]],[[]]]
=> [1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> {{1,5},{2,4},{3}}
=> 2
[[[[]]],[[]]]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> {{1,5},{2},{3},{4}}
=> 2
[[[],[],[]],[]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> {{1,5},{2,3,4}}
=> 3
[[[],[[]]],[]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> {{1},{2,5},{3,4}}
=> 2
[[[[]],[]],[]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> {{1,5},{2},{3,4}}
=> 2
[[[[],[]]],[]]
=> [1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> {{1,2},{3,5},{4}}
=> 2
[[[[[]]]],[]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> {{1},{2},{3,5},{4}}
=> 2
[[[],[],[],[]]]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> {{1,2,3,4},{5}}
=> 4
Description
The maximal size of a block of a set partition.
Matching statistic: St000392
(load all 3 compositions to match this statistic)
(load all 3 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
Mp00109: Permutations —descent word⟶ Binary words
St000392: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
St000392: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[]]
=> [.,.]
=> [1] => => ? = 1 - 1
[[],[]]
=> [.,[.,.]]
=> [2,1] => 1 => 1 = 2 - 1
[[[]]]
=> [[.,.],.]
=> [1,2] => 0 => 0 = 1 - 1
[[],[],[]]
=> [.,[.,[.,.]]]
=> [3,2,1] => 11 => 2 = 3 - 1
[[],[[]]]
=> [.,[[.,.],.]]
=> [2,3,1] => 01 => 1 = 2 - 1
[[[]],[]]
=> [[.,.],[.,.]]
=> [1,3,2] => 01 => 1 = 2 - 1
[[[],[]]]
=> [[.,[.,.]],.]
=> [2,1,3] => 10 => 1 = 2 - 1
[[[[]]]]
=> [[[.,.],.],.]
=> [1,2,3] => 00 => 0 = 1 - 1
[[],[],[],[]]
=> [.,[.,[.,[.,.]]]]
=> [4,3,2,1] => 111 => 3 = 4 - 1
[[],[],[[]]]
=> [.,[.,[[.,.],.]]]
=> [3,4,2,1] => 011 => 2 = 3 - 1
[[],[[]],[]]
=> [.,[[.,.],[.,.]]]
=> [2,4,3,1] => 011 => 2 = 3 - 1
[[],[[],[]]]
=> [.,[[.,[.,.]],.]]
=> [3,2,4,1] => 101 => 1 = 2 - 1
[[],[[[]]]]
=> [.,[[[.,.],.],.]]
=> [2,3,4,1] => 001 => 1 = 2 - 1
[[[]],[],[]]
=> [[.,.],[.,[.,.]]]
=> [1,4,3,2] => 011 => 2 = 3 - 1
[[[]],[[]]]
=> [[.,.],[[.,.],.]]
=> [1,3,4,2] => 001 => 1 = 2 - 1
[[[],[]],[]]
=> [[.,[.,.]],[.,.]]
=> [2,1,4,3] => 101 => 1 = 2 - 1
[[[[]]],[]]
=> [[[.,.],.],[.,.]]
=> [1,2,4,3] => 001 => 1 = 2 - 1
[[[],[],[]]]
=> [[.,[.,[.,.]]],.]
=> [3,2,1,4] => 110 => 2 = 3 - 1
[[[],[[]]]]
=> [[.,[[.,.],.]],.]
=> [2,3,1,4] => 010 => 1 = 2 - 1
[[[[]],[]]]
=> [[[.,.],[.,.]],.]
=> [1,3,2,4] => 010 => 1 = 2 - 1
[[[[],[]]]]
=> [[[.,[.,.]],.],.]
=> [2,1,3,4] => 100 => 1 = 2 - 1
[[[[[]]]]]
=> [[[[.,.],.],.],.]
=> [1,2,3,4] => 000 => 0 = 1 - 1
[[],[],[],[],[]]
=> [.,[.,[.,[.,[.,.]]]]]
=> [5,4,3,2,1] => 1111 => 4 = 5 - 1
[[],[],[],[[]]]
=> [.,[.,[.,[[.,.],.]]]]
=> [4,5,3,2,1] => 0111 => 3 = 4 - 1
[[],[],[[]],[]]
=> [.,[.,[[.,.],[.,.]]]]
=> [3,5,4,2,1] => 0111 => 3 = 4 - 1
[[],[],[[],[]]]
=> [.,[.,[[.,[.,.]],.]]]
=> [4,3,5,2,1] => 1011 => 2 = 3 - 1
[[],[],[[[]]]]
=> [.,[.,[[[.,.],.],.]]]
=> [3,4,5,2,1] => 0011 => 2 = 3 - 1
[[],[[]],[],[]]
=> [.,[[.,.],[.,[.,.]]]]
=> [2,5,4,3,1] => 0111 => 3 = 4 - 1
[[],[[]],[[]]]
=> [.,[[.,.],[[.,.],.]]]
=> [2,4,5,3,1] => 0011 => 2 = 3 - 1
[[],[[],[]],[]]
=> [.,[[.,[.,.]],[.,.]]]
=> [3,2,5,4,1] => 1011 => 2 = 3 - 1
[[],[[[]]],[]]
=> [.,[[[.,.],.],[.,.]]]
=> [2,3,5,4,1] => 0011 => 2 = 3 - 1
[[],[[],[],[]]]
=> [.,[[.,[.,[.,.]]],.]]
=> [4,3,2,5,1] => 1101 => 2 = 3 - 1
[[],[[],[[]]]]
=> [.,[[.,[[.,.],.]],.]]
=> [3,4,2,5,1] => 0101 => 1 = 2 - 1
[[],[[[]],[]]]
=> [.,[[[.,.],[.,.]],.]]
=> [2,4,3,5,1] => 0101 => 1 = 2 - 1
[[],[[[],[]]]]
=> [.,[[[.,[.,.]],.],.]]
=> [3,2,4,5,1] => 1001 => 1 = 2 - 1
[[],[[[[]]]]]
=> [.,[[[[.,.],.],.],.]]
=> [2,3,4,5,1] => 0001 => 1 = 2 - 1
[[[]],[],[],[]]
=> [[.,.],[.,[.,[.,.]]]]
=> [1,5,4,3,2] => 0111 => 3 = 4 - 1
[[[]],[],[[]]]
=> [[.,.],[.,[[.,.],.]]]
=> [1,4,5,3,2] => 0011 => 2 = 3 - 1
[[[]],[[]],[]]
=> [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => 0011 => 2 = 3 - 1
[[[]],[[],[]]]
=> [[.,.],[[.,[.,.]],.]]
=> [1,4,3,5,2] => 0101 => 1 = 2 - 1
[[[]],[[[]]]]
=> [[.,.],[[[.,.],.],.]]
=> [1,3,4,5,2] => 0001 => 1 = 2 - 1
[[[],[]],[],[]]
=> [[.,[.,.]],[.,[.,.]]]
=> [2,1,5,4,3] => 1011 => 2 = 3 - 1
[[[[]]],[],[]]
=> [[[.,.],.],[.,[.,.]]]
=> [1,2,5,4,3] => 0011 => 2 = 3 - 1
[[[],[]],[[]]]
=> [[.,[.,.]],[[.,.],.]]
=> [2,1,4,5,3] => 1001 => 1 = 2 - 1
[[[[]]],[[]]]
=> [[[.,.],.],[[.,.],.]]
=> [1,2,4,5,3] => 0001 => 1 = 2 - 1
[[[],[],[]],[]]
=> [[.,[.,[.,.]]],[.,.]]
=> [3,2,1,5,4] => 1101 => 2 = 3 - 1
[[[],[[]]],[]]
=> [[.,[[.,.],.]],[.,.]]
=> [2,3,1,5,4] => 0101 => 1 = 2 - 1
[[[[]],[]],[]]
=> [[[.,.],[.,.]],[.,.]]
=> [1,3,2,5,4] => 0101 => 1 = 2 - 1
[[[[],[]]],[]]
=> [[[.,[.,.]],.],[.,.]]
=> [2,1,3,5,4] => 1001 => 1 = 2 - 1
[[[[[]]]],[]]
=> [[[[.,.],.],.],[.,.]]
=> [1,2,3,5,4] => 0001 => 1 = 2 - 1
[[[],[],[],[]]]
=> [[.,[.,[.,[.,.]]]],.]
=> [4,3,2,1,5] => 1110 => 3 = 4 - 1
Description
The length of the longest run of ones in a binary word.
Matching statistic: St000485
(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
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
St000485: Permutations ⟶ ℤResult quality: 68% ●values known / values provided: 68%●distinct values known / distinct values provided: 86%
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
St000485: Permutations ⟶ ℤResult quality: 68% ●values known / values provided: 68%●distinct values known / distinct values provided: 86%
Values
[[]]
=> [.,.]
=> [1] => [1] => ? = 1
[[],[]]
=> [.,[.,.]]
=> [2,1] => [2,1] => 2
[[[]]]
=> [[.,.],.]
=> [1,2] => [1,2] => 1
[[],[],[]]
=> [.,[.,[.,.]]]
=> [3,2,1] => [2,3,1] => 3
[[],[[]]]
=> [.,[[.,.],.]]
=> [2,3,1] => [3,2,1] => 2
[[[]],[]]
=> [[.,.],[.,.]]
=> [1,3,2] => [1,3,2] => 2
[[[],[]]]
=> [[.,[.,.]],.]
=> [2,1,3] => [2,1,3] => 2
[[[[]]]]
=> [[[.,.],.],.]
=> [1,2,3] => [1,2,3] => 1
[[],[],[],[]]
=> [.,[.,[.,[.,.]]]]
=> [4,3,2,1] => [2,3,4,1] => 4
[[],[],[[]]]
=> [.,[.,[[.,.],.]]]
=> [3,4,2,1] => [2,4,3,1] => 3
[[],[[]],[]]
=> [.,[[.,.],[.,.]]]
=> [2,4,3,1] => [3,2,4,1] => 3
[[],[[],[]]]
=> [.,[[.,[.,.]],.]]
=> [3,2,4,1] => [4,3,2,1] => 2
[[],[[[]]]]
=> [.,[[[.,.],.],.]]
=> [2,3,4,1] => [4,2,3,1] => 2
[[[]],[],[]]
=> [[.,.],[.,[.,.]]]
=> [1,4,3,2] => [1,3,4,2] => 3
[[[]],[[]]]
=> [[.,.],[[.,.],.]]
=> [1,3,4,2] => [1,4,3,2] => 2
[[[],[]],[]]
=> [[.,[.,.]],[.,.]]
=> [2,1,4,3] => [2,1,4,3] => 2
[[[[]]],[]]
=> [[[.,.],.],[.,.]]
=> [1,2,4,3] => [1,2,4,3] => 2
[[[],[],[]]]
=> [[.,[.,[.,.]]],.]
=> [3,2,1,4] => [2,3,1,4] => 3
[[[],[[]]]]
=> [[.,[[.,.],.]],.]
=> [2,3,1,4] => [3,2,1,4] => 2
[[[[]],[]]]
=> [[[.,.],[.,.]],.]
=> [1,3,2,4] => [1,3,2,4] => 2
[[[[],[]]]]
=> [[[.,[.,.]],.],.]
=> [2,1,3,4] => [2,1,3,4] => 2
[[[[[]]]]]
=> [[[[.,.],.],.],.]
=> [1,2,3,4] => [1,2,3,4] => 1
[[],[],[],[],[]]
=> [.,[.,[.,[.,[.,.]]]]]
=> [5,4,3,2,1] => [2,3,4,5,1] => 5
[[],[],[],[[]]]
=> [.,[.,[.,[[.,.],.]]]]
=> [4,5,3,2,1] => [2,3,5,4,1] => 4
[[],[],[[]],[]]
=> [.,[.,[[.,.],[.,.]]]]
=> [3,5,4,2,1] => [2,4,3,5,1] => 4
[[],[],[[],[]]]
=> [.,[.,[[.,[.,.]],.]]]
=> [4,3,5,2,1] => [2,5,4,3,1] => 3
[[],[],[[[]]]]
=> [.,[.,[[[.,.],.],.]]]
=> [3,4,5,2,1] => [2,5,3,4,1] => 3
[[],[[]],[],[]]
=> [.,[[.,.],[.,[.,.]]]]
=> [2,5,4,3,1] => [3,2,4,5,1] => 4
[[],[[]],[[]]]
=> [.,[[.,.],[[.,.],.]]]
=> [2,4,5,3,1] => [3,2,5,4,1] => 3
[[],[[],[]],[]]
=> [.,[[.,[.,.]],[.,.]]]
=> [3,2,5,4,1] => [4,3,2,5,1] => 3
[[],[[[]]],[]]
=> [.,[[[.,.],.],[.,.]]]
=> [2,3,5,4,1] => [4,2,3,5,1] => 3
[[],[[],[],[]]]
=> [.,[[.,[.,[.,.]]],.]]
=> [4,3,2,5,1] => [5,3,4,2,1] => 3
[[],[[],[[]]]]
=> [.,[[.,[[.,.],.]],.]]
=> [3,4,2,5,1] => [5,4,3,2,1] => 2
[[],[[[]],[]]]
=> [.,[[[.,.],[.,.]],.]]
=> [2,4,3,5,1] => [5,2,4,3,1] => 2
[[],[[[],[]]]]
=> [.,[[[.,[.,.]],.],.]]
=> [3,2,4,5,1] => [5,3,2,4,1] => 2
[[],[[[[]]]]]
=> [.,[[[[.,.],.],.],.]]
=> [2,3,4,5,1] => [5,2,3,4,1] => 2
[[[]],[],[],[]]
=> [[.,.],[.,[.,[.,.]]]]
=> [1,5,4,3,2] => [1,3,4,5,2] => 4
[[[]],[],[[]]]
=> [[.,.],[.,[[.,.],.]]]
=> [1,4,5,3,2] => [1,3,5,4,2] => 3
[[[]],[[]],[]]
=> [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => [1,4,3,5,2] => 3
[[[]],[[],[]]]
=> [[.,.],[[.,[.,.]],.]]
=> [1,4,3,5,2] => [1,5,4,3,2] => 2
[[[]],[[[]]]]
=> [[.,.],[[[.,.],.],.]]
=> [1,3,4,5,2] => [1,5,3,4,2] => 2
[[[],[]],[],[]]
=> [[.,[.,.]],[.,[.,.]]]
=> [2,1,5,4,3] => [2,1,4,5,3] => 3
[[[[]]],[],[]]
=> [[[.,.],.],[.,[.,.]]]
=> [1,2,5,4,3] => [1,2,4,5,3] => 3
[[[],[]],[[]]]
=> [[.,[.,.]],[[.,.],.]]
=> [2,1,4,5,3] => [2,1,5,4,3] => 2
[[[[]]],[[]]]
=> [[[.,.],.],[[.,.],.]]
=> [1,2,4,5,3] => [1,2,5,4,3] => 2
[[[],[],[]],[]]
=> [[.,[.,[.,.]]],[.,.]]
=> [3,2,1,5,4] => [2,3,1,5,4] => 3
[[[],[[]]],[]]
=> [[.,[[.,.],.]],[.,.]]
=> [2,3,1,5,4] => [3,2,1,5,4] => 2
[[[[]],[]],[]]
=> [[[.,.],[.,.]],[.,.]]
=> [1,3,2,5,4] => [1,3,2,5,4] => 2
[[[[],[]]],[]]
=> [[[.,[.,.]],.],[.,.]]
=> [2,1,3,5,4] => [2,1,3,5,4] => 2
[[[[[]]]],[]]
=> [[[[.,.],.],.],[.,.]]
=> [1,2,3,5,4] => [1,2,3,5,4] => 2
[[[],[],[],[]]]
=> [[.,[.,[.,[.,.]]]],.]
=> [4,3,2,1,5] => [2,3,4,1,5] => 4
[[],[],[],[],[],[],[]]
=> [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
=> [7,6,5,4,3,2,1] => [2,3,4,5,6,7,1] => ? = 7
[[],[],[],[],[],[[]]]
=> [.,[.,[.,[.,[.,[[.,.],.]]]]]]
=> [6,7,5,4,3,2,1] => [2,3,4,5,7,6,1] => ? = 6
[[],[],[],[],[[]],[]]
=> [.,[.,[.,[.,[[.,.],[.,.]]]]]]
=> [5,7,6,4,3,2,1] => [2,3,4,6,5,7,1] => ? = 6
[[],[],[],[],[[[]]]]
=> [.,[.,[.,[.,[[[.,.],.],.]]]]]
=> [5,6,7,4,3,2,1] => [2,3,4,7,5,6,1] => ? = 5
[[],[],[],[[]],[],[]]
=> [.,[.,[.,[[.,.],[.,[.,.]]]]]]
=> [4,7,6,5,3,2,1] => [2,3,5,4,6,7,1] => ? = 6
[[],[],[],[[]],[[]]]
=> [.,[.,[.,[[.,.],[[.,.],.]]]]]
=> [4,6,7,5,3,2,1] => [2,3,5,4,7,6,1] => ? = 5
[[],[],[],[[[]]],[]]
=> [.,[.,[.,[[[.,.],.],[.,.]]]]]
=> [4,5,7,6,3,2,1] => [2,3,6,4,5,7,1] => ? = 5
[[],[],[],[[[[]]]]]
=> [.,[.,[.,[[[[.,.],.],.],.]]]]
=> [4,5,6,7,3,2,1] => [2,3,7,4,5,6,1] => ? = 4
[[],[],[[]],[],[],[]]
=> [.,[.,[[.,.],[.,[.,[.,.]]]]]]
=> [3,7,6,5,4,2,1] => [2,4,3,5,6,7,1] => ? = 6
[[],[],[[]],[],[[]]]
=> [.,[.,[[.,.],[.,[[.,.],.]]]]]
=> [3,6,7,5,4,2,1] => [2,4,3,5,7,6,1] => ? = 5
[[],[],[[]],[[]],[]]
=> [.,[.,[[.,.],[[.,.],[.,.]]]]]
=> [3,5,7,6,4,2,1] => [2,4,3,6,5,7,1] => ? = 5
[[],[],[[]],[[[]]]]
=> [.,[.,[[.,.],[[[.,.],.],.]]]]
=> [3,5,6,7,4,2,1] => [2,4,3,7,5,6,1] => ? = 4
[[],[],[[[]]],[],[]]
=> [.,[.,[[[.,.],.],[.,[.,.]]]]]
=> [3,4,7,6,5,2,1] => [2,5,3,4,6,7,1] => ? = 5
[[],[],[[[]]],[[]]]
=> [.,[.,[[[.,.],.],[[.,.],.]]]]
=> [3,4,6,7,5,2,1] => [2,5,3,4,7,6,1] => ? = 4
[[],[],[[[[]]]],[]]
=> [.,[.,[[[[.,.],.],.],[.,.]]]]
=> [3,4,5,7,6,2,1] => [2,6,3,4,5,7,1] => ? = 4
[[],[],[[[[[]]]]]]
=> [.,[.,[[[[[.,.],.],.],.],.]]]
=> [3,4,5,6,7,2,1] => [2,7,3,4,5,6,1] => ? = 3
[[],[[]],[],[],[],[]]
=> [.,[[.,.],[.,[.,[.,[.,.]]]]]]
=> [2,7,6,5,4,3,1] => [3,2,4,5,6,7,1] => ? = 6
[[],[[]],[],[],[[]]]
=> [.,[[.,.],[.,[.,[[.,.],.]]]]]
=> [2,6,7,5,4,3,1] => [3,2,4,5,7,6,1] => ? = 5
[[],[[]],[],[[]],[]]
=> [.,[[.,.],[.,[[.,.],[.,.]]]]]
=> [2,5,7,6,4,3,1] => [3,2,4,6,5,7,1] => ? = 5
[[],[[]],[],[[[]]]]
=> [.,[[.,.],[.,[[[.,.],.],.]]]]
=> [2,5,6,7,4,3,1] => [3,2,4,7,5,6,1] => ? = 4
[[],[[]],[[]],[],[]]
=> [.,[[.,.],[[.,.],[.,[.,.]]]]]
=> [2,4,7,6,5,3,1] => [3,2,5,4,6,7,1] => ? = 5
[[],[[]],[[]],[[]]]
=> [.,[[.,.],[[.,.],[[.,.],.]]]]
=> [2,4,6,7,5,3,1] => [3,2,5,4,7,6,1] => ? = 4
[[],[[]],[[[]]],[]]
=> [.,[[.,.],[[[.,.],.],[.,.]]]]
=> [2,4,5,7,6,3,1] => [3,2,6,4,5,7,1] => ? = 4
[[],[[]],[[[[]]]]]
=> [.,[[.,.],[[[[.,.],.],.],.]]]
=> [2,4,5,6,7,3,1] => [3,2,7,4,5,6,1] => ? = 3
[[],[[[]]],[],[],[]]
=> [.,[[[.,.],.],[.,[.,[.,.]]]]]
=> [2,3,7,6,5,4,1] => [4,2,3,5,6,7,1] => ? = 5
[[],[[[]]],[],[[]]]
=> [.,[[[.,.],.],[.,[[.,.],.]]]]
=> [2,3,6,7,5,4,1] => [4,2,3,5,7,6,1] => ? = 4
[[],[[[]]],[[]],[]]
=> [.,[[[.,.],.],[[.,.],[.,.]]]]
=> [2,3,5,7,6,4,1] => [4,2,3,6,5,7,1] => ? = 4
[[],[[[]]],[[[]]]]
=> [.,[[[.,.],.],[[[.,.],.],.]]]
=> [2,3,5,6,7,4,1] => [4,2,3,7,5,6,1] => ? = 3
[[],[[[[]]]],[],[]]
=> [.,[[[[.,.],.],.],[.,[.,.]]]]
=> [2,3,4,7,6,5,1] => [5,2,3,4,6,7,1] => ? = 4
[[],[[[[]]]],[[]]]
=> [.,[[[[.,.],.],.],[[.,.],.]]]
=> [2,3,4,6,7,5,1] => [5,2,3,4,7,6,1] => ? = 3
[[],[[[[[]]]]],[]]
=> [.,[[[[[.,.],.],.],.],[.,.]]]
=> [2,3,4,5,7,6,1] => [6,2,3,4,5,7,1] => ? = 3
[[[]],[[[]]],[],[]]
=> [[.,.],[[[.,.],.],[.,[.,.]]]]
=> [1,3,4,7,6,5,2] => [1,5,3,4,6,7,2] => ? = 4
[[[]],[[[]]],[[]]]
=> [[.,.],[[[.,.],.],[[.,.],.]]]
=> [1,3,4,6,7,5,2] => [1,5,3,4,7,6,2] => ? = 3
[[[]],[[[[]]]],[]]
=> [[.,.],[[[[.,.],.],.],[.,.]]]
=> [1,3,4,5,7,6,2] => [1,6,3,4,5,7,2] => ? = 3
[[[],[]],[],[],[],[]]
=> [[.,[.,.]],[.,[.,[.,[.,.]]]]]
=> [2,1,7,6,5,4,3] => [2,1,4,5,6,7,3] => ? = 5
[[[],[]],[],[],[[]]]
=> [[.,[.,.]],[.,[.,[[.,.],.]]]]
=> [2,1,6,7,5,4,3] => [2,1,4,5,7,6,3] => ? = 4
[[[],[]],[],[[]],[]]
=> [[.,[.,.]],[.,[[.,.],[.,.]]]]
=> [2,1,5,7,6,4,3] => [2,1,4,6,5,7,3] => ? = 4
[[[],[]],[],[[[]]]]
=> [[.,[.,.]],[.,[[[.,.],.],.]]]
=> [2,1,5,6,7,4,3] => [2,1,4,7,5,6,3] => ? = 3
[[[],[]],[[]],[],[]]
=> [[.,[.,.]],[[.,.],[.,[.,.]]]]
=> [2,1,4,7,6,5,3] => [2,1,5,4,6,7,3] => ? = 4
[[[],[]],[[]],[[]]]
=> [[.,[.,.]],[[.,.],[[.,.],.]]]
=> [2,1,4,6,7,5,3] => [2,1,5,4,7,6,3] => ? = 3
[[[],[]],[[[]]],[]]
=> [[.,[.,.]],[[[.,.],.],[.,.]]]
=> [2,1,4,5,7,6,3] => [2,1,6,4,5,7,3] => ? = 3
[[[],[],[]],[],[],[]]
=> [[.,[.,[.,.]]],[.,[.,[.,.]]]]
=> [3,2,1,7,6,5,4] => [2,3,1,5,6,7,4] => ? = 4
[[[],[[]]],[],[],[]]
=> [[.,[[.,.],.]],[.,[.,[.,.]]]]
=> [2,3,1,7,6,5,4] => [3,2,1,5,6,7,4] => ? = 4
[[[[],[]]],[],[],[]]
=> [[[.,[.,.]],.],[.,[.,[.,.]]]]
=> [2,1,3,7,6,5,4] => [2,1,3,5,6,7,4] => ? = 4
[[[],[],[]],[],[[]]]
=> [[.,[.,[.,.]]],[.,[[.,.],.]]]
=> [3,2,1,6,7,5,4] => [2,3,1,5,7,6,4] => ? = 3
[[[],[[]]],[],[[]]]
=> [[.,[[.,.],.]],[.,[[.,.],.]]]
=> [2,3,1,6,7,5,4] => [3,2,1,5,7,6,4] => ? = 3
[[[[],[]]],[],[[]]]
=> [[[.,[.,.]],.],[.,[[.,.],.]]]
=> [2,1,3,6,7,5,4] => [2,1,3,5,7,6,4] => ? = 3
[[[],[],[]],[[]],[]]
=> [[.,[.,[.,.]]],[[.,.],[.,.]]]
=> [3,2,1,5,7,6,4] => [2,3,1,6,5,7,4] => ? = 3
[[[],[[]]],[[]],[]]
=> [[.,[[.,.],.]],[[.,.],[.,.]]]
=> [2,3,1,5,7,6,4] => [3,2,1,6,5,7,4] => ? = 3
Description
The length of the longest cycle of a permutation.
Matching statistic: St001372
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00049: Ordered trees —to binary tree: left brother = left child⟶ Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St001372: Binary words ⟶ ℤResult quality: 60% ●values known / values provided: 60%●distinct values known / distinct values provided: 86%
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St001372: Binary words ⟶ ℤResult quality: 60% ●values known / values provided: 60%●distinct values known / distinct values provided: 86%
Values
[[]]
=> [.,.]
=> [1,0]
=> 10 => 1
[[],[]]
=> [[.,.],.]
=> [1,1,0,0]
=> 1100 => 2
[[[]]]
=> [.,[.,.]]
=> [1,0,1,0]
=> 1010 => 1
[[],[],[]]
=> [[[.,.],.],.]
=> [1,1,1,0,0,0]
=> 111000 => 3
[[],[[]]]
=> [[.,.],[.,.]]
=> [1,1,0,0,1,0]
=> 110010 => 2
[[[]],[]]
=> [[.,[.,.]],.]
=> [1,1,0,1,0,0]
=> 110100 => 2
[[[],[]]]
=> [.,[[.,.],.]]
=> [1,0,1,1,0,0]
=> 101100 => 2
[[[[]]]]
=> [.,[.,[.,.]]]
=> [1,0,1,0,1,0]
=> 101010 => 1
[[],[],[],[]]
=> [[[[.,.],.],.],.]
=> [1,1,1,1,0,0,0,0]
=> 11110000 => 4
[[],[],[[]]]
=> [[[.,.],.],[.,.]]
=> [1,1,1,0,0,0,1,0]
=> 11100010 => 3
[[],[[]],[]]
=> [[[.,.],[.,.]],.]
=> [1,1,1,0,0,1,0,0]
=> 11100100 => 3
[[],[[],[]]]
=> [[.,.],[[.,.],.]]
=> [1,1,0,0,1,1,0,0]
=> 11001100 => 2
[[],[[[]]]]
=> [[.,.],[.,[.,.]]]
=> [1,1,0,0,1,0,1,0]
=> 11001010 => 2
[[[]],[],[]]
=> [[[.,[.,.]],.],.]
=> [1,1,1,0,1,0,0,0]
=> 11101000 => 3
[[[]],[[]]]
=> [[.,[.,.]],[.,.]]
=> [1,1,0,1,0,0,1,0]
=> 11010010 => 2
[[[],[]],[]]
=> [[.,[[.,.],.]],.]
=> [1,1,0,1,1,0,0,0]
=> 11011000 => 2
[[[[]]],[]]
=> [[.,[.,[.,.]]],.]
=> [1,1,0,1,0,1,0,0]
=> 11010100 => 2
[[[],[],[]]]
=> [.,[[[.,.],.],.]]
=> [1,0,1,1,1,0,0,0]
=> 10111000 => 3
[[[],[[]]]]
=> [.,[[.,.],[.,.]]]
=> [1,0,1,1,0,0,1,0]
=> 10110010 => 2
[[[[]],[]]]
=> [.,[[.,[.,.]],.]]
=> [1,0,1,1,0,1,0,0]
=> 10110100 => 2
[[[[],[]]]]
=> [.,[.,[[.,.],.]]]
=> [1,0,1,0,1,1,0,0]
=> 10101100 => 2
[[[[[]]]]]
=> [.,[.,[.,[.,.]]]]
=> [1,0,1,0,1,0,1,0]
=> 10101010 => 1
[[],[],[],[],[]]
=> [[[[[.,.],.],.],.],.]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1111100000 => 5
[[],[],[],[[]]]
=> [[[[.,.],.],.],[.,.]]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1111000010 => 4
[[],[],[[]],[]]
=> [[[[.,.],.],[.,.]],.]
=> [1,1,1,1,0,0,0,1,0,0]
=> 1111000100 => 4
[[],[],[[],[]]]
=> [[[.,.],.],[[.,.],.]]
=> [1,1,1,0,0,0,1,1,0,0]
=> 1110001100 => 3
[[],[],[[[]]]]
=> [[[.,.],.],[.,[.,.]]]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1110001010 => 3
[[],[[]],[],[]]
=> [[[[.,.],[.,.]],.],.]
=> [1,1,1,1,0,0,1,0,0,0]
=> 1111001000 => 4
[[],[[]],[[]]]
=> [[[.,.],[.,.]],[.,.]]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1110010010 => 3
[[],[[],[]],[]]
=> [[[.,.],[[.,.],.]],.]
=> [1,1,1,0,0,1,1,0,0,0]
=> 1110011000 => 3
[[],[[[]]],[]]
=> [[[.,.],[.,[.,.]]],.]
=> [1,1,1,0,0,1,0,1,0,0]
=> 1110010100 => 3
[[],[[],[],[]]]
=> [[.,.],[[[.,.],.],.]]
=> [1,1,0,0,1,1,1,0,0,0]
=> 1100111000 => 3
[[],[[],[[]]]]
=> [[.,.],[[.,.],[.,.]]]
=> [1,1,0,0,1,1,0,0,1,0]
=> 1100110010 => 2
[[],[[[]],[]]]
=> [[.,.],[[.,[.,.]],.]]
=> [1,1,0,0,1,1,0,1,0,0]
=> 1100110100 => 2
[[],[[[],[]]]]
=> [[.,.],[.,[[.,.],.]]]
=> [1,1,0,0,1,0,1,1,0,0]
=> 1100101100 => 2
[[],[[[[]]]]]
=> [[.,.],[.,[.,[.,.]]]]
=> [1,1,0,0,1,0,1,0,1,0]
=> 1100101010 => 2
[[[]],[],[],[]]
=> [[[[.,[.,.]],.],.],.]
=> [1,1,1,1,0,1,0,0,0,0]
=> 1111010000 => 4
[[[]],[],[[]]]
=> [[[.,[.,.]],.],[.,.]]
=> [1,1,1,0,1,0,0,0,1,0]
=> 1110100010 => 3
[[[]],[[]],[]]
=> [[[.,[.,.]],[.,.]],.]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1110100100 => 3
[[[]],[[],[]]]
=> [[.,[.,.]],[[.,.],.]]
=> [1,1,0,1,0,0,1,1,0,0]
=> 1101001100 => 2
[[[]],[[[]]]]
=> [[.,[.,.]],[.,[.,.]]]
=> [1,1,0,1,0,0,1,0,1,0]
=> 1101001010 => 2
[[[],[]],[],[]]
=> [[[.,[[.,.],.]],.],.]
=> [1,1,1,0,1,1,0,0,0,0]
=> 1110110000 => 3
[[[[]]],[],[]]
=> [[[.,[.,[.,.]]],.],.]
=> [1,1,1,0,1,0,1,0,0,0]
=> 1110101000 => 3
[[[],[]],[[]]]
=> [[.,[[.,.],.]],[.,.]]
=> [1,1,0,1,1,0,0,0,1,0]
=> 1101100010 => 2
[[[[]]],[[]]]
=> [[.,[.,[.,.]]],[.,.]]
=> [1,1,0,1,0,1,0,0,1,0]
=> 1101010010 => 2
[[[],[],[]],[]]
=> [[.,[[[.,.],.],.]],.]
=> [1,1,0,1,1,1,0,0,0,0]
=> 1101110000 => 3
[[[],[[]]],[]]
=> [[.,[[.,.],[.,.]]],.]
=> [1,1,0,1,1,0,0,1,0,0]
=> 1101100100 => 2
[[[[]],[]],[]]
=> [[.,[[.,[.,.]],.]],.]
=> [1,1,0,1,1,0,1,0,0,0]
=> 1101101000 => 2
[[[[],[]]],[]]
=> [[.,[.,[[.,.],.]]],.]
=> [1,1,0,1,0,1,1,0,0,0]
=> 1101011000 => 2
[[[[[]]]],[]]
=> [[.,[.,[.,[.,.]]]],.]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1101010100 => 2
[[],[],[],[],[],[],[]]
=> [[[[[[[.,.],.],.],.],.],.],.]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> 11111110000000 => ? = 7
[[],[],[],[],[[]],[]]
=> [[[[[[.,.],.],.],.],[.,.]],.]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=> 11111100000100 => ? = 6
[[],[],[],[],[[[]]]]
=> [[[[[.,.],.],.],.],[.,[.,.]]]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> 11111000001010 => ? = 5
[[],[],[],[[]],[],[]]
=> [[[[[[.,.],.],.],[.,.]],.],.]
=> [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> 11111100001000 => ? = 6
[[],[],[],[[[]]],[]]
=> [[[[[.,.],.],.],[.,[.,.]]],.]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> 11111000010100 => ? = 5
[[],[],[],[[[[]]]]]
=> [[[[.,.],.],.],[.,[.,[.,.]]]]
=> [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
=> 11110000101010 => ? = 4
[[],[],[[]],[],[],[]]
=> [[[[[[.,.],.],[.,.]],.],.],.]
=> [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=> 11111100010000 => ? = 6
[[],[],[[]],[[]],[]]
=> [[[[[.,.],.],[.,.]],[.,.]],.]
=> [1,1,1,1,1,0,0,0,1,0,0,1,0,0]
=> 11111000100100 => ? = 5
[[],[],[[]],[[[]]]]
=> [[[[.,.],.],[.,.]],[.,[.,.]]]
=> [1,1,1,1,0,0,0,1,0,0,1,0,1,0]
=> 11110001001010 => ? = 4
[[],[],[[[]]],[],[]]
=> [[[[[.,.],.],[.,[.,.]]],.],.]
=> [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
=> 11111000101000 => ? = 5
[[],[],[[[]]],[[]]]
=> [[[[.,.],.],[.,[.,.]]],[.,.]]
=> [1,1,1,1,0,0,0,1,0,1,0,0,1,0]
=> 11110001010010 => ? = 4
[[],[],[[[[]]]],[]]
=> [[[[.,.],.],[.,[.,[.,.]]]],.]
=> [1,1,1,1,0,0,0,1,0,1,0,1,0,0]
=> 11110001010100 => ? = 4
[[],[],[[[[[]]]]]]
=> [[[.,.],.],[.,[.,[.,[.,.]]]]]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
=> 11100010101010 => ? = 3
[[],[[]],[],[],[],[]]
=> [[[[[[.,.],[.,.]],.],.],.],.]
=> [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
=> 11111100100000 => ? = 6
[[],[[]],[],[[]],[]]
=> [[[[[.,.],[.,.]],.],[.,.]],.]
=> [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> 11111001000100 => ? = 5
[[],[[]],[],[[[]]]]
=> [[[[.,.],[.,.]],.],[.,[.,.]]]
=> [1,1,1,1,0,0,1,0,0,0,1,0,1,0]
=> 11110010001010 => ? = 4
[[],[[]],[[]],[],[]]
=> [[[[[.,.],[.,.]],[.,.]],.],.]
=> [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
=> 11111001001000 => ? = 5
[[],[[]],[[]],[[]]]
=> [[[[.,.],[.,.]],[.,.]],[.,.]]
=> [1,1,1,1,0,0,1,0,0,1,0,0,1,0]
=> 11110010010010 => ? = 4
[[],[[]],[[[]]],[]]
=> [[[[.,.],[.,.]],[.,[.,.]]],.]
=> [1,1,1,1,0,0,1,0,0,1,0,1,0,0]
=> 11110010010100 => ? = 4
[[],[[]],[[[[]]]]]
=> [[[.,.],[.,.]],[.,[.,[.,.]]]]
=> [1,1,1,0,0,1,0,0,1,0,1,0,1,0]
=> 11100100101010 => ? = 3
[[],[[[]]],[],[],[]]
=> [[[[[.,.],[.,[.,.]]],.],.],.]
=> [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
=> 11111001010000 => ? = 5
[[],[[[]]],[],[[]]]
=> [[[[.,.],[.,[.,.]]],.],[.,.]]
=> [1,1,1,1,0,0,1,0,1,0,0,0,1,0]
=> 11110010100010 => ? = 4
[[],[[[]]],[[]],[]]
=> [[[[.,.],[.,[.,.]]],[.,.]],.]
=> [1,1,1,1,0,0,1,0,1,0,0,1,0,0]
=> 11110010100100 => ? = 4
[[],[[[]]],[[[]]]]
=> [[[.,.],[.,[.,.]]],[.,[.,.]]]
=> [1,1,1,0,0,1,0,1,0,0,1,0,1,0]
=> 11100101001010 => ? = 3
[[],[[[[]]]],[],[]]
=> [[[[.,.],[.,[.,[.,.]]]],.],.]
=> [1,1,1,1,0,0,1,0,1,0,1,0,0,0]
=> 11110010101000 => ? = 4
[[],[[[[]]]],[[]]]
=> [[[.,.],[.,[.,[.,.]]]],[.,.]]
=> [1,1,1,0,0,1,0,1,0,1,0,0,1,0]
=> 11100101010010 => ? = 3
[[],[[[[[]]]]],[]]
=> [[[.,.],[.,[.,[.,[.,.]]]]],.]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=> 11100101010100 => ? = 3
[[[]],[],[],[],[],[]]
=> [[[[[[.,[.,.]],.],.],.],.],.]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 11111101000000 => ? = 6
[[[]],[],[],[[]],[]]
=> [[[[[.,[.,.]],.],.],[.,.]],.]
=> [1,1,1,1,1,0,1,0,0,0,0,1,0,0]
=> 11111010000100 => ? = 5
[[[]],[],[],[[[]]]]
=> [[[[.,[.,.]],.],.],[.,[.,.]]]
=> [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
=> 11110100001010 => ? = 4
[[[]],[],[[]],[],[]]
=> [[[[[.,[.,.]],.],[.,.]],.],.]
=> [1,1,1,1,1,0,1,0,0,0,1,0,0,0]
=> 11111010001000 => ? = 5
[[[]],[],[[]],[[]]]
=> [[[[.,[.,.]],.],[.,.]],[.,.]]
=> [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
=> 11110100010010 => ? = 4
[[[]],[],[[[]]],[]]
=> [[[[.,[.,.]],.],[.,[.,.]]],.]
=> [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
=> 11110100010100 => ? = 4
[[[]],[],[[[[]]]]]
=> [[[.,[.,.]],.],[.,[.,[.,.]]]]
=> [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
=> 11101000101010 => ? = 3
[[[]],[[]],[],[],[]]
=> [[[[[.,[.,.]],[.,.]],.],.],.]
=> [1,1,1,1,1,0,1,0,0,1,0,0,0,0]
=> 11111010010000 => ? = 5
[[[]],[[]],[[]],[]]
=> [[[[.,[.,.]],[.,.]],[.,.]],.]
=> [1,1,1,1,0,1,0,0,1,0,0,1,0,0]
=> 11110100100100 => ? = 4
[[[]],[[]],[[[]]]]
=> [[[.,[.,.]],[.,.]],[.,[.,.]]]
=> [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
=> 11101001001010 => ? = 3
[[[]],[[[]]],[],[]]
=> [[[[.,[.,.]],[.,[.,.]]],.],.]
=> [1,1,1,1,0,1,0,0,1,0,1,0,0,0]
=> 11110100101000 => ? = 4
[[[]],[[[]]],[[]]]
=> [[[.,[.,.]],[.,[.,.]]],[.,.]]
=> [1,1,1,0,1,0,0,1,0,1,0,0,1,0]
=> 11101001010010 => ? = 3
[[[]],[[[[]]]],[]]
=> [[[.,[.,.]],[.,[.,[.,.]]]],.]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> 11101001010100 => ? = 3
[[[],[]],[],[],[],[]]
=> [[[[[.,[[.,.],.]],.],.],.],.]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 11111011000000 => ? = 5
[[[[]]],[],[],[],[]]
=> [[[[[.,[.,[.,.]]],.],.],.],.]
=> [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> 11111010100000 => ? = 5
[[[],[]],[],[[]],[]]
=> [[[[.,[[.,.],.]],.],[.,.]],.]
=> [1,1,1,1,0,1,1,0,0,0,0,1,0,0]
=> 11110110000100 => ? = 4
[[[[]]],[],[[]],[]]
=> [[[[.,[.,[.,.]]],.],[.,.]],.]
=> [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
=> 11110101000100 => ? = 4
[[[],[]],[],[[[]]]]
=> [[[.,[[.,.],.]],.],[.,[.,.]]]
=> [1,1,1,0,1,1,0,0,0,0,1,0,1,0]
=> 11101100001010 => ? = 3
[[[[]]],[],[[[]]]]
=> [[[.,[.,[.,.]]],.],[.,[.,.]]]
=> [1,1,1,0,1,0,1,0,0,0,1,0,1,0]
=> 11101010001010 => ? = 3
[[[],[]],[[]],[],[]]
=> [[[[.,[[.,.],.]],[.,.]],.],.]
=> [1,1,1,1,0,1,1,0,0,0,1,0,0,0]
=> 11110110001000 => ? = 4
[[[[]]],[[]],[],[]]
=> [[[[.,[.,[.,.]]],[.,.]],.],.]
=> [1,1,1,1,0,1,0,1,0,0,1,0,0,0]
=> 11110101001000 => ? = 4
[[[],[]],[[]],[[]]]
=> [[[.,[[.,.],.]],[.,.]],[.,.]]
=> [1,1,1,0,1,1,0,0,0,1,0,0,1,0]
=> 11101100010010 => ? = 3
[[[[]]],[[]],[[]]]
=> [[[.,[.,[.,.]]],[.,.]],[.,.]]
=> [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
=> 11101010010010 => ? = 3
Description
The length of a longest cyclic run of ones of a binary word.
Consider the binary word as a cyclic arrangement of ones and zeros. Then this statistic is the length of the longest continuous sequence of ones in this arrangement.
Matching statistic: St000328
(load all 10 compositions to match this statistic)
(load all 10 compositions to match this statistic)
St000328: Ordered trees ⟶ ℤResult quality: 54% ●values known / values provided: 54%●distinct values known / distinct values provided: 86%
Values
[[]]
=> 1
[[],[]]
=> 2
[[[]]]
=> 1
[[],[],[]]
=> 3
[[],[[]]]
=> 2
[[[]],[]]
=> 2
[[[],[]]]
=> 2
[[[[]]]]
=> 1
[[],[],[],[]]
=> 4
[[],[],[[]]]
=> 3
[[],[[]],[]]
=> 3
[[],[[],[]]]
=> 2
[[],[[[]]]]
=> 2
[[[]],[],[]]
=> 3
[[[]],[[]]]
=> 2
[[[],[]],[]]
=> 2
[[[[]]],[]]
=> 2
[[[],[],[]]]
=> 3
[[[],[[]]]]
=> 2
[[[[]],[]]]
=> 2
[[[[],[]]]]
=> 2
[[[[[]]]]]
=> 1
[[],[],[],[],[]]
=> 5
[[],[],[],[[]]]
=> 4
[[],[],[[]],[]]
=> 4
[[],[],[[],[]]]
=> 3
[[],[],[[[]]]]
=> 3
[[],[[]],[],[]]
=> 4
[[],[[]],[[]]]
=> 3
[[],[[],[]],[]]
=> 3
[[],[[[]]],[]]
=> 3
[[],[[],[],[]]]
=> 3
[[],[[],[[]]]]
=> 2
[[],[[[]],[]]]
=> 2
[[],[[[],[]]]]
=> 2
[[],[[[[]]]]]
=> 2
[[[]],[],[],[]]
=> 4
[[[]],[],[[]]]
=> 3
[[[]],[[]],[]]
=> 3
[[[]],[[],[]]]
=> 2
[[[]],[[[]]]]
=> 2
[[[],[]],[],[]]
=> 3
[[[[]]],[],[]]
=> 3
[[[],[]],[[]]]
=> 2
[[[[]]],[[]]]
=> 2
[[[],[],[]],[]]
=> 3
[[[],[[]]],[]]
=> 2
[[[[]],[]],[]]
=> 2
[[[[],[]]],[]]
=> 2
[[[[[]]]],[]]
=> 2
[[],[],[],[],[],[],[]]
=> ? = 7
[[],[],[],[],[],[[]]]
=> ? = 6
[[],[],[],[],[[]],[]]
=> ? = 6
[[],[],[],[],[[[]]]]
=> ? = 5
[[],[],[],[[]],[],[]]
=> ? = 6
[[],[],[],[[]],[[]]]
=> ? = 5
[[],[],[],[[[]]],[]]
=> ? = 5
[[],[],[],[[[[]]]]]
=> ? = 4
[[],[],[[]],[],[],[]]
=> ? = 6
[[],[],[[]],[],[[]]]
=> ? = 5
[[],[],[[]],[[]],[]]
=> ? = 5
[[],[],[[]],[[[]]]]
=> ? = 4
[[],[],[[[]]],[],[]]
=> ? = 5
[[],[],[[[]]],[[]]]
=> ? = 4
[[],[],[[[[]]]],[]]
=> ? = 4
[[],[],[[[[[]]]]]]
=> ? = 3
[[],[[]],[],[],[],[]]
=> ? = 6
[[],[[]],[],[],[[]]]
=> ? = 5
[[],[[]],[],[[]],[]]
=> ? = 5
[[],[[]],[],[[[]]]]
=> ? = 4
[[],[[]],[[]],[],[]]
=> ? = 5
[[],[[]],[[]],[[]]]
=> ? = 4
[[],[[]],[[[]]],[]]
=> ? = 4
[[],[[]],[[[[]]]]]
=> ? = 3
[[],[[[]]],[],[],[]]
=> ? = 5
[[],[[[]]],[],[[]]]
=> ? = 4
[[],[[[]]],[[]],[]]
=> ? = 4
[[],[[[]]],[[[]]]]
=> ? = 3
[[],[[[[]]]],[],[]]
=> ? = 4
[[],[[[[]]]],[[]]]
=> ? = 3
[[],[[[[[]]]]],[]]
=> ? = 3
[[[]],[],[],[],[],[]]
=> ? = 6
[[[]],[],[],[],[[]]]
=> ? = 5
[[[]],[],[],[[]],[]]
=> ? = 5
[[[]],[],[],[[[]]]]
=> ? = 4
[[[]],[],[[]],[],[]]
=> ? = 5
[[[]],[],[[]],[[]]]
=> ? = 4
[[[]],[],[[[]]],[]]
=> ? = 4
[[[]],[],[[[[]]]]]
=> ? = 3
[[[]],[[]],[],[],[]]
=> ? = 5
[[[]],[[]],[],[[]]]
=> ? = 4
[[[]],[[]],[[]],[]]
=> ? = 4
[[[]],[[]],[[[]]]]
=> ? = 3
[[[]],[[[]]],[],[]]
=> ? = 4
[[[]],[[[]]],[[]]]
=> ? = 3
[[[]],[[[[]]]],[]]
=> ? = 3
[[[],[]],[],[],[],[]]
=> ? = 5
[[[[]]],[],[],[],[]]
=> ? = 5
[[[],[]],[],[],[[]]]
=> ? = 4
[[[[]]],[],[],[[]]]
=> ? = 4
Description
The maximum number of child nodes in a tree.
Matching statistic: St000846
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00047: Ordered trees —to poset⟶ Posets
St000846: Posets ⟶ ℤResult quality: 54% ●values known / values provided: 54%●distinct values known / distinct values provided: 86%
St000846: Posets ⟶ ℤResult quality: 54% ●values known / values provided: 54%●distinct values known / distinct values provided: 86%
Values
[[]]
=> ([(0,1)],2)
=> 1
[[],[]]
=> ([(0,2),(1,2)],3)
=> 2
[[[]]]
=> ([(0,2),(2,1)],3)
=> 1
[[],[],[]]
=> ([(0,3),(1,3),(2,3)],4)
=> 3
[[],[[]]]
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[[[]],[]]
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[[[],[]]]
=> ([(0,3),(1,3),(3,2)],4)
=> 2
[[[[]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[[],[],[],[]]
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 4
[[],[],[[]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3
[[],[[]],[]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3
[[],[[],[]]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> 2
[[],[[[]]]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> 2
[[[]],[],[]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3
[[[]],[[]]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> 2
[[[],[]],[]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> 2
[[[[]]],[]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> 2
[[[],[],[]]]
=> ([(0,4),(1,4),(2,4),(4,3)],5)
=> 3
[[[],[[]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> 2
[[[[]],[]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> 2
[[[[],[]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> 2
[[[[[]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[[],[],[],[],[]]
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 5
[[],[],[],[[]]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> 4
[[],[],[[]],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> 4
[[],[],[[],[]]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 3
[[],[],[[[]]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> 3
[[],[[]],[],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> 4
[[],[[]],[[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> 3
[[],[[],[]],[]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 3
[[],[[[]]],[]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> 3
[[],[[],[],[]]]
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 3
[[],[[],[[]]]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> 2
[[],[[[]],[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> 2
[[],[[[],[]]]]
=> ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> 2
[[],[[[[]]]]]
=> ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> 2
[[[]],[],[],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> 4
[[[]],[],[[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> 3
[[[]],[[]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> 3
[[[]],[[],[]]]
=> ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> 2
[[[]],[[[]]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> 2
[[[],[]],[],[]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 3
[[[[]]],[],[]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> 3
[[[],[]],[[]]]
=> ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> 2
[[[[]]],[[]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> 2
[[[],[],[]],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 3
[[[],[[]]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> 2
[[[[]],[]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> 2
[[[[],[]]],[]]
=> ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> 2
[[[[[]]]],[]]
=> ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> 2
[[],[],[],[],[],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 7
[[],[],[],[],[],[[]]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
=> ? = 6
[[],[],[],[],[[]],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
=> ? = 6
[[],[],[],[],[[[]]]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
=> ? = 5
[[],[],[],[[]],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
=> ? = 6
[[],[],[],[[]],[[]]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 5
[[],[],[],[[[]]],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
=> ? = 5
[[],[],[],[[[[]]]]]
=> ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
=> ? = 4
[[],[],[[]],[],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
=> ? = 6
[[],[],[[]],[],[[]]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 5
[[],[],[[]],[[]],[]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 5
[[],[],[[]],[[[]]]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ? = 4
[[],[],[[[]]],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
=> ? = 5
[[],[],[[[]]],[[]]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ? = 4
[[],[],[[[[]]]],[]]
=> ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
=> ? = 4
[[],[],[[[[[]]]]]]
=> ([(0,7),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
=> ? = 3
[[],[[]],[],[],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
=> ? = 6
[[],[[]],[],[],[[]]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 5
[[],[[]],[],[[]],[]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 5
[[],[[]],[],[[[]]]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ? = 4
[[],[[]],[[]],[],[]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 5
[[],[[]],[[]],[[]]]
=> ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
=> ? = 4
[[],[[]],[[[]]],[]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ? = 4
[[],[[]],[[[[]]]]]
=> ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
=> ? = 3
[[],[[[]]],[],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
=> ? = 5
[[],[[[]]],[],[[]]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ? = 4
[[],[[[]]],[[]],[]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ? = 4
[[],[[[]]],[[[]]]]
=> ([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8)
=> ? = 3
[[],[[[[]]]],[],[]]
=> ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
=> ? = 4
[[],[[[[]]]],[[]]]
=> ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
=> ? = 3
[[],[[[[[]]]]],[]]
=> ([(0,7),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
=> ? = 3
[[[]],[],[],[],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
=> ? = 6
[[[]],[],[],[],[[]]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 5
[[[]],[],[],[[]],[]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 5
[[[]],[],[],[[[]]]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ? = 4
[[[]],[],[[]],[],[]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 5
[[[]],[],[[]],[[]]]
=> ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
=> ? = 4
[[[]],[],[[[]]],[]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ? = 4
[[[]],[],[[[[]]]]]
=> ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
=> ? = 3
[[[]],[[]],[],[],[]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 5
[[[]],[[]],[],[[]]]
=> ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
=> ? = 4
[[[]],[[]],[[]],[]]
=> ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
=> ? = 4
[[[]],[[]],[[[]]]]
=> ([(0,5),(1,4),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
=> ? = 3
[[[]],[[[]]],[],[]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ? = 4
[[[]],[[[]]],[[]]]
=> ([(0,5),(1,4),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
=> ? = 3
[[[]],[[[[]]]],[]]
=> ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
=> ? = 3
[[[],[]],[],[],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ? = 5
[[[[]]],[],[],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
=> ? = 5
[[[],[]],[],[],[[]]]
=> ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 4
[[[[]]],[],[],[[]]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ? = 4
Description
The maximal number of elements covering an element of a poset.
Matching statistic: St000845
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
[[]]
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1
[[],[]]
=> ([(0,2),(1,2)],3)
=> ([(0,1),(0,2)],3)
=> 2
[[[]]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1
[[],[],[]]
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3)],4)
=> 3
[[],[[]]]
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,2),(0,3),(3,1)],4)
=> 2
[[[]],[]]
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,2),(0,3),(3,1)],4)
=> 2
[[[],[]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(0,3),(3,1),(3,2)],4)
=> 2
[[[[]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[[],[],[],[]]
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4)],5)
=> 4
[[],[],[[]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(4,1)],5)
=> 3
[[],[[]],[]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(4,1)],5)
=> 3
[[],[[],[]]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(4,1),(4,2)],5)
=> 2
[[],[[[]]]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 2
[[[]],[],[]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(4,1)],5)
=> 3
[[[]],[[]]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(3,2),(4,1)],5)
=> 2
[[[],[]],[]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(4,1),(4,2)],5)
=> 2
[[[[]]],[]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 2
[[[],[],[]]]
=> ([(0,4),(1,4),(2,4),(4,3)],5)
=> ([(0,4),(4,1),(4,2),(4,3)],5)
=> 3
[[[],[[]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,4),(3,2),(4,1),(4,3)],5)
=> 2
[[[[]],[]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,4),(3,2),(4,1),(4,3)],5)
=> 2
[[[[],[]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(0,3),(3,4),(4,1),(4,2)],5)
=> 2
[[[[[]]]]]
=> ([(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)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> 5
[[],[],[],[[]]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> 4
[[],[],[[]],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> 4
[[],[],[[],[]]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> 3
[[],[],[[[]]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> 3
[[],[[]],[],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> 4
[[],[[]],[[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> 3
[[],[[],[]],[]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> 3
[[],[[[]]],[]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> 3
[[],[[],[],[]]]
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> ([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> 3
[[],[[],[[]]]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
=> 2
[[],[[[]],[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
=> 2
[[],[[[],[]]]]
=> ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> ([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
=> 2
[[],[[[[]]]]]
=> ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 2
[[[]],[],[],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> 4
[[[]],[],[[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> 3
[[[]],[[]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> 3
[[[]],[[],[]]]
=> ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> 2
[[[]],[[[]]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 2
[[[],[]],[],[]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> 3
[[[[]]],[],[]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> 3
[[[],[]],[[]]]
=> ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> 2
[[[[]]],[[]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 2
[[[],[],[]],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> ([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> 3
[[[],[[]]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
=> 2
[[[[]],[]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
=> 2
[[[[],[]]],[]]
=> ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> ([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
=> 2
[[[[[]]]],[]]
=> ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 2
[[],[],[],[],[],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7)],8)
=> ? = 7
[[],[],[],[],[],[[]]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(7,1)],8)
=> ? = 6
[[],[],[],[],[[]],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(7,1)],8)
=> ? = 6
[[],[],[],[],[[[]]]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
=> ([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8)
=> ? = 5
[[],[],[],[[]],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(7,1)],8)
=> ? = 6
[[],[],[],[[]],[[]]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8)
=> ? = 5
[[],[],[],[[[]]],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
=> ([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8)
=> ? = 5
[[],[],[],[[[[]]]]]
=> ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
=> ([(0,2),(0,3),(0,4),(0,7),(5,6),(6,1),(7,5)],8)
=> ? = 4
[[],[],[[]],[],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(7,1)],8)
=> ? = 6
[[],[],[[]],[],[[]]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8)
=> ? = 5
[[],[],[[]],[[]],[]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8)
=> ? = 5
[[],[],[[]],[[[]]]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)
=> ? = 4
[[],[],[[[]]],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
=> ([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8)
=> ? = 5
[[],[],[[[]]],[[]]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)
=> ? = 4
[[],[],[[[[]]]],[]]
=> ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
=> ([(0,2),(0,3),(0,4),(0,7),(5,6),(6,1),(7,5)],8)
=> ? = 4
[[],[],[[[[[]]]]]]
=> ([(0,7),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
=> ?
=> ? = 3
[[],[[]],[],[],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(7,1)],8)
=> ? = 6
[[],[[]],[],[],[[]]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8)
=> ? = 5
[[],[[]],[],[[]],[]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8)
=> ? = 5
[[],[[]],[],[[[]]]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)
=> ? = 4
[[],[[]],[[]],[],[]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8)
=> ? = 5
[[],[[]],[[]],[[]]]
=> ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
=> ?
=> ? = 4
[[],[[]],[[[]]],[]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)
=> ? = 4
[[],[[]],[[[[]]]]]
=> ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
=> ([(0,3),(0,6),(0,7),(4,5),(5,2),(6,4),(7,1)],8)
=> ? = 3
[[],[[[]]],[],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
=> ([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8)
=> ? = 5
[[],[[[]]],[],[[]]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)
=> ? = 4
[[],[[[]]],[[]],[]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)
=> ? = 4
[[],[[[]]],[[[]]]]
=> ([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8)
=> ([(0,3),(0,6),(0,7),(4,2),(5,1),(6,4),(7,5)],8)
=> ? = 3
[[],[[[[]]]],[],[]]
=> ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
=> ([(0,2),(0,3),(0,4),(0,7),(5,6),(6,1),(7,5)],8)
=> ? = 4
[[],[[[[]]]],[[]]]
=> ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
=> ([(0,3),(0,6),(0,7),(4,5),(5,2),(6,4),(7,1)],8)
=> ? = 3
[[],[[[[[]]]]],[]]
=> ([(0,7),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
=> ?
=> ? = 3
[[[]],[],[],[],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(7,1)],8)
=> ? = 6
[[[]],[],[],[],[[]]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8)
=> ? = 5
[[[]],[],[],[[]],[]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8)
=> ? = 5
[[[]],[],[],[[[]]]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)
=> ? = 4
[[[]],[],[[]],[],[]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8)
=> ? = 5
[[[]],[],[[]],[[]]]
=> ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
=> ?
=> ? = 4
[[[]],[],[[[]]],[]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)
=> ? = 4
[[[]],[],[[[[]]]]]
=> ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
=> ([(0,3),(0,6),(0,7),(4,5),(5,2),(6,4),(7,1)],8)
=> ? = 3
[[[]],[[]],[],[],[]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8)
=> ? = 5
[[[]],[[]],[],[[]]]
=> ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
=> ?
=> ? = 4
[[[]],[[]],[[]],[]]
=> ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
=> ?
=> ? = 4
[[[]],[[]],[[[]]]]
=> ([(0,5),(1,4),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
=> ?
=> ? = 3
[[[]],[[[]]],[],[]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)
=> ? = 4
[[[]],[[[]]],[[]]]
=> ([(0,5),(1,4),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
=> ?
=> ? = 3
[[[]],[[[[]]]],[]]
=> ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
=> ([(0,3),(0,6),(0,7),(4,5),(5,2),(6,4),(7,1)],8)
=> ? = 3
[[[],[]],[],[],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(7,1),(7,2)],8)
=> ? = 5
[[[[]]],[],[],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
=> ([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8)
=> ? = 5
[[[],[]],[],[],[[]]]
=> ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
=> ?
=> ? = 4
[[[[]]],[],[],[[]]]
=> ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
=> ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)
=> ? = 4
Description
The maximal number of elements covered by an element in a poset.
The following 6 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001235The global dimension of the corresponding Comp-Nakayama algebra. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001330The hat guessing number of a graph. St000454The largest eigenvalue of a graph if it is integral. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path.
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