Identifier
Values
[.,[.,.]] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 0
[[.,.],.] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 0
[.,[.,[.,.]]] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 0
[.,[[.,.],.]] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 0
[[.,.],[.,.]] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[.,[.,.]],.] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 0
[[[.,.],.],.] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 0
[.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[.,[.,[[.,.],.]]] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[.,[[.,.],[.,.]]] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[.,[[.,[.,.]],.]] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[.,[[[.,.],.],.]] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[.,.],[[.,.],.]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[.,[.,.]],[.,.]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[.,[.,[.,.]]],.] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[.,[[.,.],.]],.] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[[.,.],[.,.]],.] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[[.,[.,.]],.],.] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[[[.,.],.],.],.] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[.,[.,[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 1
[.,[.,[[.,[.,.]],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[.,[[.,[.,[.,.]]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[.,[[.,[[.,.],.]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[.,[[[.,.],[.,.]],.]] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 1
[.,[[[.,[.,.]],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[.,[[[[.,.],.],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[.,[.,[.,[.,.]]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[.,[.,[[.,.],.]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[.,[[.,.],[.,.]]],.] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 1
[[.,[[.,[.,.]],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[.,[[[.,.],.],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[[.,[.,[.,.]]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[[.,[[.,.],.]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[[[.,.],[.,.]],.],.] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 1
[[[[.,[.,.]],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[[[[.,.],.],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[.,[.,[.,[[.,[.,.]],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[.,[.,[[.,[.,[.,.]]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[.,[.,[[.,[[.,.],.]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[.,[.,[[[.,[.,.]],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[.,[[.,[.,[.,[.,.]]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[.,[[.,[.,[[.,.],.]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[.,[[.,[[.,[.,.]],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[.,[[.,[[[.,.],.],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[.,[[[.,[.,[.,.]]],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[.,[[[.,[[.,.],.]],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[.,[[[[.,[.,.]],.],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[.,[[[[[.,.],.],.],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[.,[.,[.,[.,[.,.]]]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[.,[.,[.,[[.,.],.]]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[.,[.,[[.,[.,.]],.]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[.,[.,[[[.,.],.],.]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[.,[[.,[.,[.,.]]],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[.,[[.,[[.,.],.]],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[.,[[[.,[.,.]],.],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[.,[[[[.,.],.],.],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[[.,[.,[.,[.,.]]]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[[.,[.,[[.,.],.]]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[[.,[[.,[.,.]],.]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[[.,[[[.,.],.],.]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[[[.,[.,[.,.]]],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[[[.,[[.,.],.]],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[[[[.,[.,.]],.],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[[[[[.,.],.],.],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 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
Description
Number of indecomposable injective modules with projective dimension 2.
Map
to poset
Description
Return the poset obtained by interpreting the tree as a Hasse diagram.
Map
order ideals
Description
The lattice of order ideals of a poset.
An order ideal $\mathcal I$ in a poset $P$ is a downward closed set, i.e., $a \in \mathcal I$ and $b \leq a$ implies $b \in \mathcal I$. This map sends a poset to the lattice of all order ideals sorted by inclusion with meet being intersection and join being union.
An order ideal $\mathcal I$ in a poset $P$ is a downward closed set, i.e., $a \in \mathcal I$ and $b \leq a$ implies $b \in \mathcal I$. This map sends a poset to the lattice of all order ideals sorted by inclusion with meet being intersection and join being union.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!