Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001038
(load all 3 compositions to match this statistic)
Mapping
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
St001038: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[],[]]
 => [1,0,1,0]
 => 2
[[[]]]
 => [1,1,0,0]
 => 1
[[],[],[]]
 => [1,0,1,0,1,0]
 => 3
[[],[[]]]
 => [1,0,1,1,0,0]
 => 1
[[[]],[]]
 => [1,1,0,0,1,0]
 => 1
[[[],[]]]
 => [1,1,0,1,0,0]
 => 1
[[[[]]]]
 => [1,1,1,0,0,0]
 => 2
[[],[],[],[]]
 => [1,0,1,0,1,0,1,0]
 => 4
[[],[],[[]]]
 => [1,0,1,0,1,1,0,0]
 => 1
[[],[[]],[]]
 => [1,0,1,1,0,0,1,0]
 => 2
[[],[[],[]]]
 => [1,0,1,1,0,1,0,0]
 => 1
[[],[[[]]]]
 => [1,0,1,1,1,0,0,0]
 => 2
[[[]],[],[]]
 => [1,1,0,0,1,0,1,0]
 => 1
[[[]],[[]]]
 => [1,1,0,0,1,1,0,0]
 => 1
[[[],[]],[]]
 => [1,1,0,1,0,0,1,0]
 => 1
[[[[]]],[]]
 => [1,1,1,0,0,0,1,0]
 => 2
[[[],[],[]]]
 => [1,1,0,1,0,1,0,0]
 => 1
[[[],[[]]]]
 => [1,1,0,1,1,0,0,0]
 => 1
[[[[]],[]]]
 => [1,1,1,0,0,1,0,0]
 => 1
[[[[],[]]]]
 => [1,1,1,0,1,0,0,0]
 => 3
[[[[[]]]]]
 => [1,1,1,1,0,0,0,0]
 => 2
[[],[],[],[],[]]
 => [1,0,1,0,1,0,1,0,1,0]
 => 5
[[],[],[],[[]]]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1
[[],[],[[]],[]]
 => [1,0,1,0,1,1,0,0,1,0]
 => 2
[[],[],[[],[]]]
 => [1,0,1,0,1,1,0,1,0,0]
 => 1
[[],[],[[[]]]]
 => [1,0,1,0,1,1,1,0,0,0]
 => 2
[[],[[]],[],[]]
 => [1,0,1,1,0,0,1,0,1,0]
 => 2
[[],[[]],[[]]]
 => [1,0,1,1,0,0,1,1,0,0]
 => 1
[[],[[],[]],[]]
 => [1,0,1,1,0,1,0,0,1,0]
 => 1
[[],[[[]]],[]]
 => [1,0,1,1,1,0,0,0,1,0]
 => 3
[[],[[],[],[]]]
 => [1,0,1,1,0,1,0,1,0,0]
 => 1
[[],[[],[[]]]]
 => [1,0,1,1,0,1,1,0,0,0]
 => 2
[[],[[[]],[]]]
 => [1,0,1,1,1,0,0,1,0,0]
 => 1
[[],[[[],[]]]]
 => [1,0,1,1,1,0,1,0,0,0]
 => 3
[[],[[[[]]]]]
 => [1,0,1,1,1,1,0,0,0,0]
 => 2
[[[]],[],[],[]]
 => [1,1,0,0,1,0,1,0,1,0]
 => 1
[[[]],[],[[]]]
 => [1,1,0,0,1,0,1,1,0,0]
 => 1
[[[]],[[]],[]]
 => [1,1,0,0,1,1,0,0,1,0]
 => 1
[[[]],[[],[]]]
 => [1,1,0,0,1,1,0,1,0,0]
 => 1
[[[]],[[[]]]]
 => [1,1,0,0,1,1,1,0,0,0]
 => 1
[[[],[]],[],[]]
 => [1,1,0,1,0,0,1,0,1,0]
 => 1
[[[[]]],[],[]]
 => [1,1,1,0,0,0,1,0,1,0]
 => 2
[[[],[]],[[]]]
 => [1,1,0,1,0,0,1,1,0,0]
 => 1
[[[[]]],[[]]]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1
[[[],[],[]],[]]
 => [1,1,0,1,0,1,0,0,1,0]
 => 1
[[[],[[]]],[]]
 => [1,1,0,1,1,0,0,0,1,0]
 => 1
[[[[]],[]],[]]
 => [1,1,1,0,0,1,0,0,1,0]
 => 2
[[[[],[]]],[]]
 => [1,1,1,0,1,0,0,0,1,0]
 => 3
[[[[[]]]],[]]
 => [1,1,1,1,0,0,0,0,1,0]
 => 2
[[[],[],[],[]]]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
Description
The minimal height of a column in the parallelogram polyomino associated with the Dyck path.
Matching statistic: St000700
Mapping
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
St000700: Ordered trees ⟶ ℤResult quality: 76% ●values known / values provided: 76%●distinct values known / distinct values provided: 88%
Values
[[],[]]
 => [1,0,1,0]
 => [1,1,0,0]
 => [[[]]]
 => 2
[[[]]]
 => [1,1,0,0]
 => [1,0,1,0]
 => [[],[]]
 => 1
[[],[],[]]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => [[[[]]]]
 => 3
[[],[[]]]
 => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => [[[]],[]]
 => 1
[[[]],[]]
 => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => [[],[[]]]
 => 1
[[[],[]]]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => [[],[],[]]
 => 1
[[[[]]]]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => [[[],[]]]
 => 2
[[],[],[],[]]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => [[[[[]]]]]
 => 4
[[],[],[[]]]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => [[[[]]],[]]
 => 1
[[],[[]],[]]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => [[[]],[[]]]
 => 2
[[],[[],[]]]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => [[[]],[],[]]
 => 1
[[],[[[]]]]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => [[[[]],[]]]
 => 2
[[[]],[],[]]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => [[],[[[]]]]
 => 1
[[[]],[[]]]
 => [1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0]
 => [[],[[]],[]]
 => 1
[[[],[]],[]]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0]
 => [[],[],[[]]]
 => 1
[[[[]]],[]]
 => [1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => [[[],[[]]]]
 => 2
[[[],[],[]]]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [[],[],[],[]]
 => 1
[[[],[[]]]]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0]
 => [[],[[],[]]]
 => 1
[[[[]],[]]]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => [[[],[]],[]]
 => 1
[[[[],[]]]]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => [[[[],[]]]]
 => 3
[[[[[]]]]]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => [[[],[],[]]]
 => 2
[[],[],[],[],[]]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => 5
[[],[],[],[[]]]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => [[[[[]]]],[]]
 => 1
[[],[],[[]],[]]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [[[[]]],[[]]]
 => 2
[[],[],[[],[]]]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => [[[[]]],[],[]]
 => 1
[[],[],[[[]]]]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [[[[[]]],[]]]
 => 2
[[],[[]],[],[]]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [[[]],[[[]]]]
 => 2
[[],[[]],[[]]]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [[[]],[[]],[]]
 => 1
[[],[[],[]],[]]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [[[]],[],[[]]]
 => 1
[[],[[[]]],[]]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [[[[]],[[]]]]
 => 3
[[],[[],[],[]]]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => [[[]],[],[],[]]
 => 1
[[],[[],[[]]]]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => [[[]],[[],[]]]
 => 2
[[],[[[]],[]]]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => [[[[]],[]],[]]
 => 1
[[],[[[],[]]]]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [[[[[]],[]]]]
 => 3
[[],[[[[]]]]]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[[[]],[],[]]]
 => 2
[[[]],[],[],[]]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [[],[[[[]]]]]
 => 1
[[[]],[],[[]]]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [[],[[[]]],[]]
 => 1
[[[]],[[]],[]]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [[],[[]],[[]]]
 => 1
[[[]],[[],[]]]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [[],[[]],[],[]]
 => 1
[[[]],[[[]]]]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[],[[[]],[]]]
 => 1
[[[],[]],[],[]]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [[],[],[[[]]]]
 => 1
[[[[]]],[],[]]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [[[],[[[]]]]]
 => 2
[[[],[]],[[]]]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [[],[],[[]],[]]
 => 1
[[[[]]],[[]]]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => [[[],[[]]],[]]
 => 1
[[[],[],[]],[]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => [[],[],[],[[]]]
 => 1
[[[],[[]]],[]]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => [[],[[],[[]]]]
 => 1
[[[[]],[]],[]]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => [[[],[]],[[]]]
 => 2
[[[[],[]]],[]]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [[[[],[[]]]]]
 => 3
[[[[[]]]],[]]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [[[],[],[[]]]]
 => 2
[[[],[],[],[]]]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [[],[],[],[],[]]
 => 1
[[],[],[],[],[],[],[],[]]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => [[[[[[[[[]]]]]]]]]
 => ? = 8
[[],[],[],[],[],[[]],[]]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [[[[[[[]]]]]],[[]]]
 => ? = 2
[[],[],[],[],[],[[],[]]]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
 => [[[[[[[]]]]]],[],[]]
 => ? = 1
[[],[],[],[],[],[[[]]]]
 => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
 => [[[[[[[[]]]]]],[]]]
 => ? = 2
[[],[],[],[],[[]],[],[]]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
 => [[[[[[]]]]],[[[]]]]
 => ? = 3
[[],[],[],[],[[]],[[]]]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
 => [[[[[[]]]]],[[]],[]]
 => ? = 1
[[],[],[],[],[[],[]],[]]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
 => [[[[[[]]]]],[],[[]]]
 => ? = 1
[[],[],[],[],[[[]]],[]]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
 => [[[[[[[]]]]],[[]]]]
 => ? = 3
[[],[],[],[],[[],[],[]]]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
 => [[[[[[]]]]],[],[],[]]
 => ? = 1
[[],[],[],[],[[],[[]]]]
 => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
 => [[[[[[]]]]],[[],[]]]
 => ? = 2
[[],[],[],[],[[[]],[]]]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
 => [[[[[[[]]]]],[]],[]]
 => ? = 1
[[],[],[],[],[[[],[]]]]
 => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
 => [[[[[[[[]]]]],[]]]]
 => ? = 3
[[],[],[],[],[[[[]]]]]
 => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
 => [[[[[[[]]]]],[],[]]]
 => ? = 2
[[],[],[],[[]],[],[],[]]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
 => [[[[[]]]],[[[[]]]]]
 => ? = 4
[[],[],[],[[]],[],[[]]]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
 => [[[[[]]]],[[[]]],[]]
 => ? = 1
[[],[],[],[[]],[[]],[]]
 => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
 => [[[[[]]]],[[]],[[]]]
 => ? = 2
[[],[],[],[[]],[[],[]]]
 => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
 => [[[[[]]]],[[]],[],[]]
 => ? = 1
[[],[],[],[[]],[[[]]]]
 => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
 => [[[[[]]]],[[[]],[]]]
 => ? = 2
[[],[],[],[[],[]],[],[]]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
 => [[[[[]]]],[],[[[]]]]
 => ? = 1
[[],[],[],[[[]]],[],[]]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
 => [[[[[[]]]],[[[]]]]]
 => ? = 4
[[],[],[],[[],[]],[[]]]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
 => [[[[[]]]],[],[[]],[]]
 => ? = 1
[[],[],[],[[[]]],[[]]]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
 => [[[[[[]]]],[[]]],[]]
 => ? = 1
[[],[],[],[[],[],[]],[]]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
 => [[[[[]]]],[],[],[[]]]
 => ? = 1
[[],[],[],[[],[[]]],[]]
 => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
 => [[[[[]]]],[[],[[]]]]
 => ? = 2
[[],[],[],[[[]],[]],[]]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
 => [[[[[[]]]],[]],[[]]]
 => ? = 2
[[],[],[],[[[],[]]],[]]
 => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
 => [[[[[[[]]]],[[]]]]]
 => ? = 4
[[],[],[],[[[[]]]],[]]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
 => [[[[[[]]]],[],[[]]]]
 => ? = 2
[[],[],[],[[],[],[],[]]]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
 => [[[[[]]]],[],[],[],[]]
 => ? = 1
[[],[],[],[[],[],[[]]]]
 => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
 => [[[[[]]]],[],[[],[]]]
 => ? = 1
[[],[],[],[[],[[]],[]]]
 => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
 => [[[[[]]]],[[],[]],[]]
 => ? = 1
[[],[],[],[[],[[],[]]]]
 => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
 => [[[[[]]]],[[[],[]]]]
 => ? = 3
[[],[],[],[[],[[[]]]]]
 => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
 => [[[[[]]]],[[],[],[]]]
 => ? = 2
[[],[],[],[[[]],[],[]]]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
 => [[[[[[]]]],[]],[],[]]
 => ? = 1
[[],[],[],[[[]],[[]]]]
 => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
 => [[[[[[]]]],[[]],[]]]
 => ? = 2
[[],[],[],[[[],[]],[]]]
 => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
 => [[[[[[[]]]],[]]],[]]
 => ? = 1
[[],[],[],[[[[]]],[]]]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
 => [[[[[[]]]],[],[]],[]]
 => ? = 1
[[],[],[],[[[],[],[]]]]
 => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
 => [[[[[[[[]]]],[]]]]]
 => ? = 4
[[],[],[],[[[],[[]]]]]
 => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
 => [[[[[[[]]]],[]],[]]]
 => ? = 2
[[],[],[],[[[[]],[]]]]
 => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
 => [[[[[[]]]],[[],[]]]]
 => ? = 3
[[],[],[],[[[[],[]]]]]
 => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
 => [[[[[[]]]],[],[],[]]]
 => ? = 2
[[],[],[],[[[[[]]]]]]
 => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
 => [[[[[[[]]]],[],[]]]]
 => ? = 3
[[],[],[[]],[],[],[],[]]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
 => [[[[]]],[[[[[]]]]]]
 => ? = 3
[[],[],[[]],[],[],[[]]]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
 => [[[[]]],[[[[]]]],[]]
 => ? = 1
[[],[],[[]],[],[[]],[]]
 => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
 => [[[[]]],[[[]]],[[]]]
 => ? = 2
[[],[],[[]],[],[[],[]]]
 => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
 => [[[[]]],[[[]]],[],[]]
 => ? = 1
[[],[],[[]],[],[[[]]]]
 => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
 => [[[[]]],[[[[]]],[]]]
 => ? = 2
[[],[],[[]],[[]],[],[]]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
 => [[[[]]],[[]],[[[]]]]
 => ? = 2
[[],[],[[]],[[]],[[]]]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
 => [[[[]]],[[]],[[]],[]]
 => ? = 1
[[],[],[[]],[[],[]],[]]
 => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
 => [[[[]]],[[]],[],[[]]]
 => ? = 1
[[],[],[[]],[[[]]],[]]
 => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
 => [[[[]]],[[[]],[[]]]]
 => ? = 3
Description
The protection number of an ordered tree. This is the minimal distance from the root to a leaf.
Matching statistic: St000908
Mapping
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
St000908: Posets ⟶ ℤResult quality: 36% ●values known / values provided: 36%●distinct values known / distinct values provided: 88%
Values
[[],[]]
 => [1,0,1,0]
 => [1,1,0,0]
 => ([],2)
 => 2
[[[]]]
 => [1,1,0,0]
 => [1,0,1,0]
 => ([(0,1)],2)
 => 1
[[],[],[]]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ([],3)
 => 3
[[],[[]]]
 => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => ([(0,1),(0,2)],3)
 => 1
[[[]],[]]
 => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => ([(0,2),(1,2)],3)
 => 1
[[[],[]]]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => ([(0,2),(2,1)],3)
 => 1
[[[[]]]]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => ([(1,2)],3)
 => 2
[[],[],[],[]]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ([],4)
 => 4
[[],[],[[]]]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => ([(0,1),(0,2),(0,3)],4)
 => 1
[[],[[]],[]]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
[[],[[],[]]]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => ([(0,3),(3,1),(3,2)],4)
 => 1
[[],[[[]]]]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => ([(1,2),(1,3)],4)
 => 2
[[[]],[],[]]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => ([(0,3),(1,3),(2,3)],4)
 => 1
[[[]],[[]]]
 => [1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[[],[]],[]]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0]
 => ([(0,3),(1,3),(3,2)],4)
 => 1
[[[[]]],[]]
 => [1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => ([(1,3),(2,3)],4)
 => 2
[[[],[],[]]]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ([(0,3),(2,1),(3,2)],4)
 => 1
[[[],[[]]]]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0]
 => ([(0,3),(1,2),(2,3)],4)
 => 1
[[[[]],[]]]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(3,1)],4)
 => 1
[[[[],[]]]]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => ([(2,3)],4)
 => 3
[[[[[]]]]]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => ([(0,3),(1,2),(1,3)],4)
 => 2
[[],[],[],[],[]]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ([],5)
 => 5
[[],[],[],[[]]]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => 1
[[],[],[[]],[]]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => 2
[[],[],[[],[]]]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ([(0,4),(4,1),(4,2),(4,3)],5)
 => 1
[[],[],[[[]]]]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => ([(1,2),(1,3),(1,4)],5)
 => 2
[[],[[]],[],[]]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
[[],[[]],[[]]]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 1
[[],[[],[]],[]]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => ([(0,4),(1,4),(4,2),(4,3)],5)
 => 1
[[],[[[]]],[]]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 3
[[],[[],[],[]]]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ([(0,3),(3,4),(4,1),(4,2)],5)
 => 1
[[],[[],[[]]]]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => 2
[[],[[[]],[]]]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => 1
[[],[[[],[]]]]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => ([(2,3),(2,4)],5)
 => 3
[[],[[[[]]]]]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => 2
[[[]],[],[],[]]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
[[[]],[],[[]]]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1
[[[]],[[]],[]]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => 1
[[[]],[[],[]]]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
[[[]],[[[]]]]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1
[[[],[]],[],[]]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => ([(0,4),(1,4),(2,4),(4,3)],5)
 => 1
[[[[]]],[],[]]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => ([(1,4),(2,4),(3,4)],5)
 => 2
[[[],[]],[[]]]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
[[[[]]],[[]]]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 1
[[[],[],[]],[]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => 1
[[[],[[]]],[]]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => 1
[[[[]],[]],[]]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => 2
[[[[],[]]],[]]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => ([(2,4),(3,4)],5)
 => 3
[[[[[]]]],[]]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
[[[],[],[],[]]]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[[],[],[],[],[[]],[]]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)
 => ? = 2
[[],[],[],[[]],[],[]]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
 => ? = 3
[[],[],[],[[[]]],[]]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
 => ? = 3
[[],[],[],[[[[]]]]]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)
 => ? = 2
[[],[],[[]],[[],[]]]
 => [1,0,1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
 => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1),(3,2)],7)
 => ? = 1
[[],[],[[]],[[[]]]]
 => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,1,0,0]
 => ([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ? = 2
[[],[],[[[]]],[],[]]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
 => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ? = 4
[[],[],[[[],[]]],[]]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,1,1,0,0,0,0]
 => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ? = 4
[[],[],[[[[]]]],[]]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,1,0,0,0]
 => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
 => ? = 2
[[],[],[[],[],[],[]]]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => ([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7)
 => ? = 1
[[],[],[[],[],[[]]]]
 => [1,0,1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,1,1,0,0,0,1,0,1,1,0,1,0,0]
 => ([(0,6),(1,2),(2,6),(6,3),(6,4),(6,5)],7)
 => ? = 1
[[],[],[[],[[]],[]]]
 => [1,0,1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1)],7)
 => ? = 1
[[],[],[[],[[],[]]]]
 => [1,0,1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,1,0,0,0]
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
 => ? = 3
[[],[],[[[]],[],[]]]
 => [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0,1,0]
 => ([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7)
 => ? = 1
[[],[],[[[]],[[]]]]
 => [1,0,1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,1,0,0]
 => ([(0,2),(0,3),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6)],7)
 => ? = 2
[[],[],[[[],[[]]]]]
 => [1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,1,0,0]
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)
 => ? = 2
[[],[],[[[[]],[]]]]
 => [1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,1,0,0,0,1,1,0,1,0,0,0]
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
 => ? = 3
[[],[],[[[[],[]]]]]
 => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,1,0,0]
 => ([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5)],7)
 => ? = 2
[[],[],[[[[[]]]]]]
 => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
 => ? = 3
[[],[[]],[],[[]],[]]
 => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 2
[[],[[]],[],[[[]]]]
 => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,1,0,0]
 => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 2
[[],[[]],[[],[],[]]]
 => [1,0,1,1,0,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
 => ([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)
 => ? = 1
[[],[[]],[[],[[]]]]
 => [1,0,1,1,0,0,1,1,0,1,1,0,0,0]
 => [1,1,0,0,1,1,0,0,1,1,0,1,0,0]
 => ([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
 => ? = 2
[[],[[]],[[[[]]]]]
 => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,0,1,1,1,0,0,1,0,1,0,0]
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 2
[[],[[[]]],[[]],[]]
 => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0,1,1,0,0]
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(5,2),(5,3),(6,2),(6,3)],7)
 => ? = 2
[[],[[],[]],[[],[]]]
 => [1,0,1,1,0,1,0,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
 => ([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)
 => ? = 1
[[],[[],[]],[[[]]]]
 => [1,0,1,1,0,1,0,0,1,1,1,0,0,0]
 => [1,1,0,0,1,0,1,1,1,0,0,1,0,0]
 => ([(0,6),(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7)
 => ? = 1
[[],[[[]]],[[[]]]]
 => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,1,0,0]
 => ([(0,5),(0,6),(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 2
[[],[[],[],[]],[[]]]
 => [1,0,1,1,0,1,0,1,0,0,1,1,0,0]
 => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
 => ([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
 => ? = 1
[[],[[[],[]],[]],[]]
 => [1,0,1,1,1,0,1,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0,1,1,0,0]
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(6,2),(6,3)],7)
 => ? = 2
[[],[[[],[[]]]],[]]
 => [1,0,1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,1,0,0,0]
 => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
 => ? = 3
[[],[[[[[]]]]],[]]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,1,0,0,0,0]
 => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ? = 3
[[],[[],[],[],[],[]]]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7)
 => ? = 1
[[],[[],[],[],[[]]]]
 => [1,0,1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,1,0,0,1,0,1,0,1,1,0,1,0,0]
 => ([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7)
 => ? = 1
[[],[[],[[]],[],[]]]
 => [1,0,1,1,0,1,1,0,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,1,0,0,1,0,1,0]
 => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7)
 => ? = 1
[[],[[],[[]],[[]]]]
 => [1,0,1,1,0,1,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,1,0,1,1,0,0,1,0,0]
 => ([(0,2),(0,3),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7)
 => ? = 2
[[],[[],[[],[]],[]]]
 => [1,0,1,1,0,1,1,0,1,0,0,1,0,0]
 => [1,1,0,0,1,1,1,0,1,0,0,0,1,0]
 => ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1)],7)
 => ? = 1
[[],[[],[[[]]],[]]]
 => [1,0,1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,1,0,0,1,1,0,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7)
 => ? = 1
[[],[[],[[[],[]]]]]
 => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,1,0,0,1,1,0,1,0,1,0,1,0,0]
 => ([(0,2),(0,6),(1,5),(1,6),(2,5),(5,3),(5,4),(6,3),(6,4)],7)
 => ? = 2
[[],[[],[[[[]]]]]]
 => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,0,0,1,1,1,0,1,0,1,0,0,0]
 => ([(0,5),(0,6),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 2
[[],[[[]],[],[],[]]]
 => [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0,1,0]
 => ([(0,4),(4,6),(5,2),(5,3),(6,1),(6,5)],7)
 => ? = 1
[[],[[[]],[],[[]]]]
 => [1,0,1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0,1,1,0,1,0,0]
 => ([(0,5),(0,6),(1,4),(4,5),(4,6),(6,2),(6,3)],7)
 => ? = 2
[[],[[[]],[[]],[]]]
 => [1,0,1,1,1,0,0,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0,1,0]
 => ([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7)
 => ? = 1
[[],[[[]],[[[]]]]]
 => [1,0,1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,1,0,0,1,0,1,0,0]
 => ([(0,5),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(6,3),(6,4)],7)
 => ? = 2
[[],[[[],[]],[],[]]]
 => [1,0,1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0,1,0,1,0]
 => ([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7)
 => ? = 1
[[],[[[[]]],[],[]]]
 => [1,0,1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,1,0,0,1,0,1,0]
 => ([(0,4),(2,5),(2,6),(3,1),(3,5),(3,6),(4,2),(4,3)],7)
 => ? = 1
[[],[[[],[]],[[]]]]
 => [1,0,1,1,1,0,1,0,0,1,1,0,0,0]
 => [1,1,1,1,0,0,1,1,0,0,0,1,0,0]
 => ([(0,5),(0,6),(1,2),(1,3),(1,4),(4,5),(4,6)],7)
 => ? = 2
[[],[[[[]]],[[]]]]
 => [1,0,1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,1,0,0]
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ? = 2
[[],[[[[],[]]],[]]]
 => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,1),(3,6)],7)
 => ? = 1
[[],[[[],[],[[]]]]]
 => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
 => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)
 => ? = 2
Description
The length of the shortest maximal antichain in a poset.
Matching statistic: St001481
(load all 3 compositions to match this statistic)
Mapping
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001481: Dyck paths ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 75%
Values
[[],[]]
 => [1,0,1,0]
 => [1,1,0,0]
 => 2
[[[]]]
 => [1,1,0,0]
 => [1,0,1,0]
 => 1
[[],[],[]]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 3
[[],[[]]]
 => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1
[[[]],[]]
 => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => 1
[[[],[]]]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => 1
[[[[]]]]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => 2
[[],[],[],[]]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 4
[[],[],[[]]]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[[],[[]],[]]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[[],[[],[]]]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => 1
[[],[[[]]]]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
[[[]],[],[]]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => 1
[[[]],[[]]]
 => [1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0]
 => 1
[[[],[]],[]]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0]
 => 1
[[[[]]],[]]
 => [1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => 2
[[[],[],[]]]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => 1
[[[],[[]]]]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0]
 => 1
[[[[]],[]]]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 1
[[[[],[]]]]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[[[[[]]]]]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => 2
[[],[],[],[],[]]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 5
[[],[],[],[[]]]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
[[],[],[[]],[]]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 2
[[],[],[[],[]]]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => 1
[[],[],[[[]]]]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[[],[[]],[],[]]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 2
[[],[[]],[[]]]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 1
[[],[[],[]],[]]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => 1
[[],[[[]]],[]]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => 3
[[],[[],[],[]]]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 1
[[],[[],[[]]]]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => 2
[[],[[[]],[]]]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => 1
[[],[[[],[]]]]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[[],[[[[]]]]]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => 2
[[[]],[],[],[]]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1
[[[]],[],[[]]]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 1
[[[]],[[]],[]]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 1
[[[]],[[],[]]]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => 1
[[[]],[[[]]]]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 1
[[[],[]],[],[]]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => 1
[[[[]]],[],[]]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => 2
[[[],[]],[[]]]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 1
[[[[]]],[[]]]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 1
[[[],[],[]],[]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1
[[[],[[]]],[]]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => 1
[[[[]],[]],[]]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => 2
[[[[],[]]],[]]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => 3
[[[[[]]]],[]]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 2
[[[],[],[],[]]]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => 1
[[],[],[],[],[],[],[]]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 7
[[],[],[],[],[],[[]]]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 1
[[],[],[],[],[[]],[]]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 2
[[],[],[],[],[[],[]]]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 1
[[],[],[],[],[[[]]]]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => ? = 2
[[],[],[],[[]],[],[]]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3
[[],[],[],[[]],[[]]]
 => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 1
[[],[],[],[[],[]],[]]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
 => ? = 1
[[],[],[],[[[]]],[]]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => ? = 3
[[],[],[],[[],[],[]]]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => ? = 1
[[],[],[],[[],[[]]]]
 => [1,0,1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,1,0,0]
 => ? = 2
[[],[],[],[[[]],[]]]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => ? = 1
[[],[],[],[[[],[]]]]
 => [1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[[],[],[],[[[[]]]]]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
 => ? = 2
[[],[],[[]],[],[],[]]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 3
[[],[],[[]],[],[[]]]
 => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 1
[[],[],[[]],[[]],[]]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
 => ? = 2
[[],[],[[]],[[],[]]]
 => [1,0,1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
 => ? = 1
[[],[],[[]],[[[]]]]
 => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,1,0,0]
 => ? = 2
[[],[],[[],[]],[],[]]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
 => ? = 1
[[],[],[[[]]],[],[]]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
 => ? = 4
[[],[],[[],[]],[[]]]
 => [1,0,1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
 => ? = 1
[[],[],[[[]]],[[]]]
 => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0,1,0]
 => ? = 1
[[],[],[[],[],[]],[]]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
 => ? = 1
[[],[],[[],[[]]],[]]
 => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,1,1,0,0,0]
 => ? = 2
[[],[],[[[]],[]],[]]
 => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0,1,1,0,0]
 => ? = 2
[[],[],[[[],[]]],[]]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,1,1,0,0,0,0]
 => ? = 4
[[],[],[[[[]]]],[]]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,1,0,0,0]
 => ? = 2
[[],[],[[],[],[],[]]]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => ? = 1
[[],[],[[],[],[[]]]]
 => [1,0,1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,1,1,0,0,0,1,0,1,1,0,1,0,0]
 => ? = 1
[[],[],[[],[[]],[]]]
 => [1,0,1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,1,0,0,1,0]
 => ? = 1
[[],[],[[],[[],[]]]]
 => [1,0,1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,1,0,0,0]
 => ? = 3
[[],[],[[],[[[]]]]]
 => [1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,1,1,0,0,0,1,1,0,1,0,1,0,0]
 => ? = 2
[[],[],[[[]],[],[]]]
 => [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0,1,0]
 => ? = 1
[[],[],[[[]],[[]]]]
 => [1,0,1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,1,0,0]
 => ? = 2
[[],[],[[[],[]],[]]]
 => [1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => ? = 1
[[],[],[[[[]]],[]]]
 => [1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0,1,0]
 => ? = 1
[[],[],[[[],[],[]]]]
 => [1,0,1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[[],[],[[[],[[]]]]]
 => [1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,1,0,0]
 => ? = 2
[[],[],[[[[]],[]]]]
 => [1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,1,0,0,0,1,1,0,1,0,0,0]
 => ? = 3
[[],[],[[[[],[]]]]]
 => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,1,0,0]
 => ? = 2
[[],[],[[[[[]]]]]]
 => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[[],[[]],[],[],[],[]]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => ? = 2
[[],[[]],[],[],[[]]]
 => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 1
[[],[[]],[],[[]],[]]
 => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
 => ? = 2
[[],[[]],[],[[],[]]]
 => [1,0,1,1,0,0,1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 1
[[],[[]],[],[[[]]]]
 => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,1,0,0]
 => ? = 2
[[],[[]],[[]],[],[]]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 2
[[],[[]],[[]],[[]]]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => ? = 1
[[],[[]],[[],[]],[]]
 => [1,0,1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
 => ? = 1
Description
The minimal height of a peak of a Dyck path.