Identifier
Values
[[]] => [1,0] => 0
[[],[]] => [1,0,1,0] => 1
[[[]]] => [1,1,0,0] => 0
[[],[],[]] => [1,0,1,0,1,0] => 2
[[],[[]]] => [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] => 0
[[],[],[],[]] => [1,0,1,0,1,0,1,0] => 3
[[],[],[[]]] => [1,0,1,0,1,1,0,0] => 2
[[],[[]],[]] => [1,0,1,1,0,0,1,0] => 1
[[],[[],[]]] => [1,0,1,1,0,1,0,0] => 2
[[],[[[]]]] => [1,0,1,1,1,0,0,0] => 1
[[[]],[],[]] => [1,1,0,0,1,0,1,0] => 2
[[[]],[[]]] => [1,1,0,0,1,1,0,0] => 1
[[[],[]],[]] => [1,1,0,1,0,0,1,0] => 2
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => 1
[[[],[],[]]] => [1,1,0,1,0,1,0,0] => 2
[[[],[[]]]] => [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] => 1
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => 0
[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => 4
[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => 3
[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => 2
[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => 3
[[],[],[[[]]]] => [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] => 2
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => 1
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => 3
[[],[[],[[]]]] => [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] => 2
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => 3
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => 2
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => 1
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => 2
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => 1
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => 3
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => 2
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => 2
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => 1
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => 3
[[[],[[]]],[]] => [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] => 2
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => 1
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => 2
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => 2
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => 2
[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => 2
[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => 1
[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => 2
[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => 1
[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => 2
[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => 1
[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => 2
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => 1
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => 1
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => 1
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => 0
[[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => 3
[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => 3
[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[],[[]],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 3
[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 1
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2
[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 3
[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 2
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => 2
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 2
[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => 2
[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => 2
[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
>>> Load all 196 entries. <<<
[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => 1
[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 2
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 1
[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 2
[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 3
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 2
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => 2
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 1
[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3
[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => 1
[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => 3
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => 3
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => 2
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => 3
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => 1
[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => 2
[[[],[[],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => 2
[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => 2
[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => 2
[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => 2
[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => 2
[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => 2
[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[[[[[],[[]]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra.
See http://www.findstat.org/DyckPaths/NakayamaAlgebras.
Map
to Dyck path
Description
Return the Dyck path of the corresponding ordered tree induced by the recurrence of the Catalan numbers, see wikipedia:Catalan_number.
This sends the maximal height of the Dyck path to the depth of the tree.