Identifier
-
Mp00013:
Binary trees
—to poset⟶
Posets
St001879: Posets ⟶ ℤ
Values
=>
Cc0010;cc-rep-0
Cc0014;cc-rep
[.,[.,[.,.]]]=>([(0,2),(2,1)],3)=>2
[.,[[.,.],.]]=>([(0,2),(2,1)],3)=>2
[[.,[.,.]],.]=>([(0,2),(2,1)],3)=>2
[[[.,.],.],.]=>([(0,2),(2,1)],3)=>2
[.,[.,[.,[.,.]]]]=>([(0,3),(2,1),(3,2)],4)=>3
[.,[.,[[.,.],.]]]=>([(0,3),(2,1),(3,2)],4)=>3
[.,[[.,[.,.]],.]]=>([(0,3),(2,1),(3,2)],4)=>3
[.,[[[.,.],.],.]]=>([(0,3),(2,1),(3,2)],4)=>3
[[.,[.,[.,.]]],.]=>([(0,3),(2,1),(3,2)],4)=>3
[[.,[[.,.],.]],.]=>([(0,3),(2,1),(3,2)],4)=>3
[[[.,[.,.]],.],.]=>([(0,3),(2,1),(3,2)],4)=>3
[[[[.,.],.],.],.]=>([(0,3),(2,1),(3,2)],4)=>3
[.,[.,[.,[.,[.,.]]]]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[.,[.,[.,[[.,.],.]]]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[.,[.,[[.,[.,.]],.]]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[.,[.,[[[.,.],.],.]]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[.,[[.,[.,[.,.]]],.]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[.,[[.,[[.,.],.]],.]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[.,[[[.,[.,.]],.],.]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[.,[[[[.,.],.],.],.]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[[.,[.,[.,[.,.]]]],.]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[[.,[.,[[.,.],.]]],.]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[[.,[[.,[.,.]],.]],.]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[[.,[[[.,.],.],.]],.]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[[[.,[.,[.,.]]],.],.]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[[[.,[[.,.],.]],.],.]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[[[[.,[.,.]],.],.],.]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[[[[[.,.],.],.],.],.]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[.,[.,[.,[.,[.,[.,.]]]]]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[.,[.,[.,[.,[[.,.],.]]]]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[.,[.,[.,[[.,[.,.]],.]]]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[.,[.,[.,[[[.,.],.],.]]]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[.,[.,[[.,[.,[.,.]]],.]]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[.,[.,[[.,[[.,.],.]],.]]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[.,[.,[[[.,[.,.]],.],.]]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[.,[.,[[[[.,.],.],.],.]]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[.,[[.,[.,[.,[.,.]]]],.]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[.,[[.,[.,[[.,.],.]]],.]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[.,[[.,[[.,[.,.]],.]],.]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[.,[[.,[[[.,.],.],.]],.]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[.,[[[.,[.,[.,.]]],.],.]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[.,[[[.,[[.,.],.]],.],.]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[.,[[[[.,[.,.]],.],.],.]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[.,[[[[[.,.],.],.],.],.]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[[.,[.,[.,[.,[.,.]]]]],.]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[[.,[.,[.,[[.,.],.]]]],.]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[[.,[.,[[.,[.,.]],.]]],.]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[[.,[.,[[[.,.],.],.]]],.]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[[.,[[.,[.,[.,.]]],.]],.]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[[.,[[.,[[.,.],.]],.]],.]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[[.,[[[.,[.,.]],.],.]],.]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[[.,[[[[.,.],.],.],.]],.]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[[[.,[.,[.,[.,.]]]],.],.]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[[[.,[.,[[.,.],.]]],.],.]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[[[.,[[[.,.],.],.]],.],.]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[[[[.,[.,[.,.]]],.],.],.]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[[[[.,[[.,.],.]],.],.],.]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[[[[[.,[.,.]],.],.],.],.]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[[[[[[.,.],.],.],.],.],.]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[.,[.,[[[[.,.],.],.],.]]]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[.,[[.,[[[.,.],.],.]],.]]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[.,[[[.,[[.,.],.]],.],.]]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[.,[[[[.,[.,.]],.],.],.]]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[.,[[[[[.,.],.],.],.],.]]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[[.,[.,[[[.,.],.],.]]],.]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[[.,[[.,[[.,.],.]],.]],.]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[[.,[[[.,[.,.]],.],.]],.]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[[.,[[[[.,.],.],.],.]],.]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[[[.,[.,[[.,.],.]]],.],.]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[[[.,[[.,[.,.]],.]],.],.]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[[[.,[[[.,.],.],.]],.],.]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[[[[.,[.,[.,.]]],.],.],.]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[[[[.,[[.,.],.]],.],.],.]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[[[[[.,[.,.]],.],.],.],.]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[.,[[[[[[.,.],.],.],.],.],.]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[.,[.,[.,[[[.,.],.],.]]]],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[.,[.,[[.,[[.,.],.]],.]]],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[.,[.,[[[.,[.,.]],.],.]]],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[.,[.,[[[[.,.],.],.],.]]],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[.,[[.,[.,[[.,.],.]]],.]],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[.,[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[.,[[.,[[[.,.],.],.]],.]],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[.,[[[.,[.,[.,.]]],.],.]],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[.,[[[.,[[.,.],.]],.],.]],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[.,[[[[.,[.,.]],.],.],.]],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[.,[[[[[.,.],.],.],.],.]],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[[.,[.,[.,[[.,.],.]]]],.],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[[.,[.,[[.,[.,.]],.]]],.],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[[.,[.,[[[.,.],.],.]]],.],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[[.,[[[[.,.],.],.],.]],.],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[[[.,[.,[[.,.],.]]],.],.],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[[[.,[[[.,.],.],.]],.],.],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[[[[.,[[.,.],.]],.],.],.],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[[[[[.,[.,.]],.],.],.],.],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[[[[[[[.,.],.],.],.],.],.],.]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
search for individual values
searching the database for the individual values of this statistic
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Map
to poset
Description
Return the poset obtained by interpreting the tree as a Hasse diagram.
searching the database
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