Identifier
Values
[.,.] => ([],1) => ([],1) => 1
[.,[.,.]] => ([(0,1)],2) => ([(0,1)],2) => 2
[[.,.],.] => ([(0,1)],2) => ([(0,1)],2) => 2
[.,[.,[.,.]]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 6
[.,[[.,.],.]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 6
[[.,.],[.,.]] => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 3
[[.,[.,.]],.] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 6
[[[.,.],.],.] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 6
[.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 24
[.,[.,[[.,.],.]]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 24
[.,[[.,.],[.,.]]] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(3,1),(3,2)],4) => 12
[.,[[.,[.,.]],.]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 24
[.,[[[.,.],.],.]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 24
[[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(3,1)],4) => 8
[[.,.],[[.,.],.]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(3,1)],4) => 8
[[.,[.,.]],[.,.]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(3,1)],4) => 8
[[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(3,1)],4) => 8
[[.,[.,[.,.]]],.] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 24
[[.,[[.,.],.]],.] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 24
[[[.,.],[.,.]],.] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(3,1),(3,2)],4) => 12
[[[.,[.,.]],.],.] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 24
[[[[.,.],.],.],.] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 24
[.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[.,[.,[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,3),(3,4),(4,1),(4,2)],5) => 60
[.,[.,[[.,[.,.]],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[.,[[.,.],[.,[.,.]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,4),(3,2),(4,1),(4,3)],5) => 40
[.,[[.,.],[[.,.],.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,4),(3,2),(4,1),(4,3)],5) => 40
[.,[[.,[.,.]],[.,.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,4),(3,2),(4,1),(4,3)],5) => 40
[.,[[[.,.],.],[.,.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,4),(3,2),(4,1),(4,3)],5) => 40
[.,[[.,[.,[.,.]]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[.,[[.,[[.,.],.]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[.,[[[.,.],[.,.]],.]] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,3),(3,4),(4,1),(4,2)],5) => 60
[.,[[[.,[.,.]],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[.,[[[[.,.],.],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(0,4),(3,1),(4,3)],5) => 30
[[.,.],[.,[[.,.],.]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(0,4),(3,1),(4,3)],5) => 30
[[.,.],[[.,.],[.,.]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => 15
[[.,.],[[.,[.,.]],.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(0,4),(3,1),(4,3)],5) => 30
[[.,.],[[[.,.],.],.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(0,4),(3,1),(4,3)],5) => 30
[[.,[.,.]],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,3),(0,4),(3,2),(4,1)],5) => 20
[[.,[.,.]],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,3),(0,4),(3,2),(4,1)],5) => 20
[[[.,.],.],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,3),(0,4),(3,2),(4,1)],5) => 20
[[[.,.],.],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,3),(0,4),(3,2),(4,1)],5) => 20
[[.,[.,[.,.]]],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(0,4),(3,1),(4,3)],5) => 30
[[.,[[.,.],.]],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(0,4),(3,1),(4,3)],5) => 30
[[[.,.],[.,.]],[.,.]] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => 15
[[[.,[.,.]],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(0,4),(3,1),(4,3)],5) => 30
[[[[.,.],.],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(0,4),(3,1),(4,3)],5) => 30
[[.,[.,[.,[.,.]]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[[.,[.,[[.,.],.]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[[.,[[.,.],[.,.]]],.] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,3),(3,4),(4,1),(4,2)],5) => 60
[[.,[[.,[.,.]],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[[.,[[[.,.],.],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[[[.,.],[.,[.,.]]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,4),(3,2),(4,1),(4,3)],5) => 40
[[[.,.],[[.,.],.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,4),(3,2),(4,1),(4,3)],5) => 40
[[[.,[.,.]],[.,.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,4),(3,2),(4,1),(4,3)],5) => 40
[[[[.,.],.],[.,.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,4),(3,2),(4,1),(4,3)],5) => 40
[[[.,[.,[.,.]]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[[[.,[[.,.],.]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[[[[.,.],[.,.]],.],.] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,3),(3,4),(4,1),(4,2)],5) => 60
[[[[.,[.,.]],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[[[[[.,.],.],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 720
[.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 720
[.,[.,[.,[[.,.],[.,.]]]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => 360
[.,[.,[.,[[.,[.,.]],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 720
[.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 720
[.,[.,[[.,.],[.,[.,.]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 240
[.,[.,[[.,.],[[.,.],.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 240
[.,[.,[[.,[.,.]],[.,.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 240
[.,[.,[[[.,.],.],[.,.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 240
[.,[.,[[.,[.,[.,.]]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 720
[.,[.,[[.,[[.,.],.]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 720
[.,[.,[[[.,.],[.,.]],.]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => 360
[.,[.,[[[.,[.,.]],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 720
[.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 720
[.,[[.,.],[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 180
[.,[[.,.],[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 180
[.,[[.,.],[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 90
[.,[[.,.],[[.,[.,.]],.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 180
[.,[[.,.],[[[.,.],.],.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 180
[.,[[.,[.,.]],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => 120
[.,[[.,[.,.]],[[.,.],.]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => 120
[.,[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => 120
[.,[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => 120
[.,[[.,[.,[.,.]]],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 180
[.,[[.,[[.,.],.]],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 180
[.,[[[.,.],[.,.]],[.,.]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 90
[.,[[[.,[.,.]],.],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 180
[.,[[[[.,.],.],.],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 180
[.,[[.,[.,[.,[.,.]]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 720
[.,[[.,[.,[[.,.],.]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 720
[.,[[.,[[.,.],[.,.]]],.]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => 360
[.,[[.,[[.,[.,.]],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 720
[.,[[.,[[[.,.],.],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 720
[.,[[[.,.],[.,[.,.]]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 240
[.,[[[.,.],[[.,.],.]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 240
[.,[[[.,[.,.]],[.,.]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 240
[.,[[[[.,.],.],[.,.]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 240
>>> Load all 197 entries. <<<
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
The product of the sizes of the principal order filters in a poset.
Map
to poset
Description
Return the poset obtained by interpreting the tree as a Hasse diagram.
Map
dual poset
Description
The dual of a poset.
The dual (or opposite) of a poset $(\mathcal P,\leq)$ is the poset $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.
The dual (or opposite) of a poset $(\mathcal P,\leq)$ is the poset $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.
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!