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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001813
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
Description
The product of the sizes of the principal order filters in a poset.
Matching statistic: St000411
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(load all 3 compositions to match this statistic)
St000411: Binary trees ⟶ ℤResult quality: 96% ●values known / values provided: 99%●distinct values known / distinct values provided: 96%
Values
[.,.]
=> ? = 1
[.,[.,.]]
=> 2
[[.,.],.]
=> 2
[.,[.,[.,.]]]
=> 6
[.,[[.,.],.]]
=> 6
[[.,.],[.,.]]
=> 3
[[.,[.,.]],.]
=> 6
[[[.,.],.],.]
=> 6
[.,[.,[.,[.,.]]]]
=> 24
[.,[.,[[.,.],.]]]
=> 24
[.,[[.,.],[.,.]]]
=> 12
[.,[[.,[.,.]],.]]
=> 24
[.,[[[.,.],.],.]]
=> 24
[[.,.],[.,[.,.]]]
=> 8
[[.,.],[[.,.],.]]
=> 8
[[.,[.,.]],[.,.]]
=> 8
[[[.,.],.],[.,.]]
=> 8
[[.,[.,[.,.]]],.]
=> 24
[[.,[[.,.],.]],.]
=> 24
[[[.,.],[.,.]],.]
=> 12
[[[.,[.,.]],.],.]
=> 24
[[[[.,.],.],.],.]
=> 24
[.,[.,[.,[.,[.,.]]]]]
=> 120
[.,[.,[.,[[.,.],.]]]]
=> 120
[.,[.,[[.,.],[.,.]]]]
=> 60
[.,[.,[[.,[.,.]],.]]]
=> 120
[.,[.,[[[.,.],.],.]]]
=> 120
[.,[[.,.],[.,[.,.]]]]
=> 40
[.,[[.,.],[[.,.],.]]]
=> 40
[.,[[.,[.,.]],[.,.]]]
=> 40
[.,[[[.,.],.],[.,.]]]
=> 40
[.,[[.,[.,[.,.]]],.]]
=> 120
[.,[[.,[[.,.],.]],.]]
=> 120
[.,[[[.,.],[.,.]],.]]
=> 60
[.,[[[.,[.,.]],.],.]]
=> 120
[.,[[[[.,.],.],.],.]]
=> 120
[[.,.],[.,[.,[.,.]]]]
=> 30
[[.,.],[.,[[.,.],.]]]
=> 30
[[.,.],[[.,.],[.,.]]]
=> 15
[[.,.],[[.,[.,.]],.]]
=> 30
[[.,.],[[[.,.],.],.]]
=> 30
[[.,[.,.]],[.,[.,.]]]
=> 20
[[.,[.,.]],[[.,.],.]]
=> 20
[[[.,.],.],[.,[.,.]]]
=> 20
[[[.,.],.],[[.,.],.]]
=> 20
[[.,[.,[.,.]]],[.,.]]
=> 30
[[.,[[.,.],.]],[.,.]]
=> 30
[[[.,.],[.,.]],[.,.]]
=> 15
[[[.,[.,.]],.],[.,.]]
=> 30
[[[[.,.],.],.],[.,.]]
=> 30
[[.,[.,[.,[.,.]]]],.]
=> 120
Description
The tree factorial of a binary tree.
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