Identifier
Values
[.,.] => [1,0] => 2
[.,[.,.]] => [1,1,0,0] => 3
[[.,.],.] => [1,0,1,0] => 3
[.,[.,[.,.]]] => [1,1,1,0,0,0] => 4
[.,[[.,.],.]] => [1,1,0,1,0,0] => 4
[[.,.],[.,.]] => [1,0,1,1,0,0] => 4
[[.,[.,.]],.] => [1,1,0,0,1,0] => 4
[[[.,.],.],.] => [1,0,1,0,1,0] => 3
[.,[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0] => 5
[.,[.,[[.,.],.]]] => [1,1,1,0,1,0,0,0] => 5
[.,[[.,.],[.,.]]] => [1,1,0,1,1,0,0,0] => 5
[.,[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0] => 5
[.,[[[.,.],.],.]] => [1,1,0,1,0,1,0,0] => 4
[[.,.],[.,[.,.]]] => [1,0,1,1,1,0,0,0] => 5
[[.,.],[[.,.],.]] => [1,0,1,1,0,1,0,0] => 3
[[.,[.,.]],[.,.]] => [1,1,0,0,1,1,0,0] => 5
[[[.,.],.],[.,.]] => [1,0,1,0,1,1,0,0] => 4
[[.,[.,[.,.]]],.] => [1,1,1,0,0,0,1,0] => 5
[[.,[[.,.],.]],.] => [1,1,0,1,0,0,1,0] => 4
[[[.,.],[.,.]],.] => [1,0,1,1,0,0,1,0] => 5
[[[.,[.,.]],.],.] => [1,1,0,0,1,0,1,0] => 4
[[[[.,.],.],.],.] => [1,0,1,0,1,0,1,0] => 4
[.,[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0] => 6
[.,[.,[.,[[.,.],.]]]] => [1,1,1,1,0,1,0,0,0,0] => 6
[.,[.,[[.,.],[.,.]]]] => [1,1,1,0,1,1,0,0,0,0] => 6
[.,[.,[[.,[.,.]],.]]] => [1,1,1,1,0,0,1,0,0,0] => 6
[.,[.,[[[.,.],.],.]]] => [1,1,1,0,1,0,1,0,0,0] => 5
[.,[[.,.],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,0] => 6
[.,[[.,.],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,0] => 4
[.,[[.,[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,0] => 6
[.,[[[.,.],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,0] => 5
[.,[[.,[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,0,0] => 6
[.,[[.,[[.,.],.]],.]] => [1,1,1,0,1,0,0,1,0,0] => 5
[.,[[[.,.],[.,.]],.]] => [1,1,0,1,1,0,0,1,0,0] => 4
[.,[[[.,[.,.]],.],.]] => [1,1,1,0,0,1,0,1,0,0] => 5
[.,[[[[.,.],.],.],.]] => [1,1,0,1,0,1,0,1,0,0] => 4
[[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0] => 6
[[.,.],[.,[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,0] => 3
[[.,.],[[.,.],[.,.]]] => [1,0,1,1,0,1,1,0,0,0] => 4
[[.,.],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => 6
[[.,.],[[[.,.],.],.]] => [1,0,1,1,0,1,0,1,0,0] => 5
[[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0] => 6
[[.,[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0] => 4
[[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => 5
[[[.,.],.],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0] => 4
[[.,[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,0,0] => 6
[[.,[[.,.],.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0] => 5
[[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => 6
[[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0] => 5
[[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0] => 5
[[.,[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,0,1,0] => 6
[[.,[.,[[.,.],.]]],.] => [1,1,1,0,1,0,0,0,1,0] => 5
[[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,0,1,0] => 6
[[.,[[.,[.,.]],.]],.] => [1,1,1,0,0,1,0,0,1,0] => 5
[[.,[[[.,.],.],.]],.] => [1,1,0,1,0,1,0,0,1,0] => 5
[[[.,.],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,0] => 6
[[[.,.],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,0] => 4
[[[.,[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0] => 6
[[[[.,.],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0] => 5
[[[.,[.,[.,.]]],.],.] => [1,1,1,0,0,0,1,0,1,0] => 5
[[[.,[[.,.],.]],.],.] => [1,1,0,1,0,0,1,0,1,0] => 5
[[[[.,.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,0] => 5
[[[[.,[.,.]],.],.],.] => [1,1,0,0,1,0,1,0,1,0] => 5
[[[[[.,.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0] => 5
[.,[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[.,[.,[.,[.,[[.,.],.]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => 7
[.,[.,[.,[[.,.],[.,.]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[.,[.,[.,[[.,[.,.]],.]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => 7
[.,[.,[.,[[[.,.],.],.]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => 6
[.,[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[.,[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => 5
[.,[.,[[.,[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[.,[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => 6
[.,[.,[[.,[.,[.,.]]],.]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => 7
[.,[.,[[.,[[.,.],.]],.]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => 6
[.,[.,[[[.,.],[.,.]],.]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => 5
[.,[.,[[[.,[.,.]],.],.]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => 6
[.,[.,[[[[.,.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => 5
[.,[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[.,[[.,.],[.,[[.,.],.]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => 4
[.,[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => 5
[.,[[.,.],[[.,[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => 4
[.,[[.,.],[[[.,.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[.,[[.,[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => 7
[.,[[.,[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => 5
[.,[[[.,.],.],[.,[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => 6
[.,[[[.,.],.],[[.,.],.]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[.,[[.,[.,[.,.]]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => 7
[.,[[.,[[.,.],.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => 6
[.,[[[.,.],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => 5
[.,[[[.,[.,.]],.],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => 6
[.,[[[[.,.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => 5
[.,[[.,[.,[.,[.,.]]]],.]] => [1,1,1,1,1,0,0,0,0,1,0,0] => 7
[.,[[.,[.,[[.,.],.]]],.]] => [1,1,1,1,0,1,0,0,0,1,0,0] => 6
[.,[[.,[[.,.],[.,.]]],.]] => [1,1,1,0,1,1,0,0,0,1,0,0] => 5
[.,[[.,[[.,[.,.]],.]],.]] => [1,1,1,1,0,0,1,0,0,1,0,0] => 6
[.,[[.,[[[.,.],.],.]],.]] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5
[.,[[[.,.],[.,[.,.]]],.]] => [1,1,0,1,1,1,0,0,0,1,0,0] => 7
[.,[[[.,.],[[.,.],.]],.]] => [1,1,0,1,1,0,1,0,0,1,0,0] => 6
[.,[[[.,[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,0,0] => 5
[.,[[[[.,.],.],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
>>> Load all 196 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [1,1,1,1,0,0,0,1,0,1,0,0] => 6
[.,[[[.,[[.,.],.]],.],.]] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5
[.,[[[[.,.],[.,.]],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,0] => 6
[.,[[[[.,[.,.]],.],.],.]] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[.,[[[[[.,.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[[.,.],[.,[.,[[.,.],.]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[[.,.],[.,[[.,.],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[[.,.],[.,[[.,[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => 7
[[.,.],[.,[[[.,.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => 6
[[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => 5
[[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => 5
[[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => 7
[[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => 6
[[.,.],[[.,[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => 7
[[.,.],[[.,[[.,.],.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
[[.,.],[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => 4
[[.,.],[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => 6
[[.,.],[[[[.,.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => 5
[[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 7
[[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => 5
[[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 7
[[.,[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 6
[[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
[[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 5
[[[.,.],.],[[.,[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,0,0] => 6
[[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => 6
[[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 7
[[.,[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 5
[[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 6
[[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 5
[[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 7
[[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 5
[[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 6
[[[.,[.,.]],.],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 5
[[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
[[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 5
[[.,[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 7
[[.,[.,[[.,.],.]]],[.,.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 6
[[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 7
[[.,[[.,[.,.]],.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 6
[[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 6
[[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 7
[[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 5
[[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 7
[[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 6
[[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 6
[[[.,[[.,.],.]],.],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 6
[[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
[[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
[[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
[[.,[.,[.,[.,[.,.]]]]],.] => [1,1,1,1,1,0,0,0,0,0,1,0] => 7
[[.,[.,[.,[[.,.],.]]]],.] => [1,1,1,1,0,1,0,0,0,0,1,0] => 6
[[.,[.,[[.,.],[.,.]]]],.] => [1,1,1,0,1,1,0,0,0,0,1,0] => 7
[[.,[.,[[.,[.,.]],.]]],.] => [1,1,1,1,0,0,1,0,0,0,1,0] => 6
[[.,[.,[[[.,.],.],.]]],.] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,0,1,0] => 7
[[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,0,0,1,0] => 5
[[.,[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,0,1,0] => 7
[[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
[[.,[[.,[.,[.,.]]],.]],.] => [1,1,1,1,0,0,0,1,0,0,1,0] => 6
[[.,[[.,[[.,.],.]],.]],.] => [1,1,1,0,1,0,0,1,0,0,1,0] => 6
[[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,0,0,1,0,0,1,0] => 5
[[.,[[[.,[.,.]],.],.]],.] => [1,1,1,0,0,1,0,1,0,0,1,0] => 6
[[.,[[[[.,.],.],.],.]],.] => [1,1,0,1,0,1,0,1,0,0,1,0] => 5
[[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0] => 7
[[[.,.],[.,[[.,.],.]]],.] => [1,0,1,1,1,0,1,0,0,0,1,0] => 4
[[[.,.],[[.,.],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,0,1,0] => 5
[[[.,.],[[.,[.,.]],.]],.] => [1,0,1,1,1,0,0,1,0,0,1,0] => 6
[[[.,.],[[[.,.],.],.]],.] => [1,0,1,1,0,1,0,1,0,0,1,0] => 6
[[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => 7
[[[.,[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,0] => 5
[[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
[[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => 5
[[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0] => 7
[[[.,[[.,.],.]],[.,.]],.] => [1,1,0,1,0,0,1,1,0,0,1,0] => 6
[[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => 7
[[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
[[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
[[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
[[[.,[.,[[.,.],.]]],.],.] => [1,1,1,0,1,0,0,0,1,0,1,0] => 6
[[[.,[[.,.],[.,.]]],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0] => 6
[[[.,[[.,[.,.]],.]],.],.] => [1,1,1,0,0,1,0,0,1,0,1,0] => 6
[[[.,[[[.,.],.],.]],.],.] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
[[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
[[[[.,.],[[.,.],.]],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0] => 5
[[[[.,[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0] => 6
[[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => 5
[[[[.,[.,[.,.]]],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
[[[[.,[[.,.],.]],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0] => 6
[[[[[.,.],[.,.]],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
[[[[[.,[.,.]],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
[[[[[[.,.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
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Description
Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra.
Map
to Tamari-corresponding Dyck path
Description
Return the Dyck path associated with a binary tree in consistency with the Tamari order on Dyck words and binary trees.
The bijection is defined recursively as follows:
  • a leaf is associated with an empty Dyck path,
  • a tree with children $l,r$ is associated with the Dyck word $T(l) 1 T(r) 0$ where $T(l)$ and $T(r)$ are the images of this bijection to $l$ and $r$.