Identifier
Values
[[]] => [1,0] => 1
[[],[]] => [1,0,1,0] => 2
[[[]]] => [1,1,0,0] => 3
[[],[],[]] => [1,0,1,0,1,0] => 3
[[],[[]]] => [1,0,1,1,0,0] => 4
[[[]],[]] => [1,1,0,0,1,0] => 4
[[[],[]]] => [1,1,0,1,0,0] => 5
[[[[]]]] => [1,1,1,0,0,0] => 6
[[],[],[],[]] => [1,0,1,0,1,0,1,0] => 4
[[],[],[[]]] => [1,0,1,0,1,1,0,0] => 5
[[],[[]],[]] => [1,0,1,1,0,0,1,0] => 5
[[],[[],[]]] => [1,0,1,1,0,1,0,0] => 6
[[],[[[]]]] => [1,0,1,1,1,0,0,0] => 7
[[[]],[],[]] => [1,1,0,0,1,0,1,0] => 5
[[[]],[[]]] => [1,1,0,0,1,1,0,0] => 6
[[[],[]],[]] => [1,1,0,1,0,0,1,0] => 6
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => 7
[[[],[],[]]] => [1,1,0,1,0,1,0,0] => 7
[[[],[[]]]] => [1,1,0,1,1,0,0,0] => 8
[[[[]],[]]] => [1,1,1,0,0,1,0,0] => 8
[[[[],[]]]] => [1,1,1,0,1,0,0,0] => 9
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => 10
[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => 5
[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => 6
[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => 6
[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => 7
[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => 8
[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => 6
[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => 7
[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => 7
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => 8
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => 8
[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => 9
[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => 9
[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => 10
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => 11
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => 6
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => 7
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => 7
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => 8
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => 9
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => 7
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => 8
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => 8
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => 9
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => 8
[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => 9
[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => 9
[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => 10
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => 11
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => 9
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => 10
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => 10
[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => 11
[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => 12
[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => 10
[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => 11
[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => 11
[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => 12
[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => 12
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => 13
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => 13
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => 14
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => 15
[[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 7
[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => 7
[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 8
[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 9
[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => 7
[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 8
[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => 8
[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => 9
[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => 9
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 10
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => 10
[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => 11
[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 12
[[],[[]],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 7
[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 8
[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 8
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 9
[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 10
[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 8
[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => 9
[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 9
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 10
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 9
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => 10
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 10
[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => 11
[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => 12
[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => 10
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => 11
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => 11
[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => 12
[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => 13
[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => 11
[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => 12
[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => 12
[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => 13
>>> Load all 196 entries. <<<
[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => 13
[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => 14
[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => 14
[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => 15
[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 16
[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 7
[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 8
[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 8
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 9
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 10
[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 8
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 9
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 9
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 10
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 10
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => 11
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 11
[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => 12
[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 13
[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 8
[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 9
[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 9
[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 10
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 9
[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 10
[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 10
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 11
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 11
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 12
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 9
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 10
[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 10
[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => 11
[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => 12
[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 10
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 11
[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 11
[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 12
[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 13
[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 10
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => 11
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 11
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => 12
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => 13
[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 11
[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 12
[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 12
[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 13
[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => 13
[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => 14
[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 14
[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => 15
[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => 16
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => 11
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => 12
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => 12
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => 13
[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => 14
[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => 12
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => 13
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => 13
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => 14
[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => 14
[[[],[[],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => 15
[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => 15
[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => 16
[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => 17
[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => 12
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => 13
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => 13
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => 14
[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => 15
[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => 13
[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => 14
[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => 14
[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => 15
[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => 14
[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => 15
[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => 15
[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => 16
[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => 17
[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => 15
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => 16
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => 16
[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => 17
[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => 18
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => 16
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => 17
[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => 17
[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => 18
[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => 18
[[[[[],[[]]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => 19
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => 19
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => 20
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => 21
search for individual values
searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
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Description
The vector space dimension of the space of module homomorphisms between J and itself when J denotes the Jacobson radical of the corresponding Nakayama algebra.
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.