Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001879
Mp00072: Permutations binary search tree: left to rightBinary trees
Mp00017: Binary trees to 312-avoiding permutationPermutations
Mp00065: Permutations permutation posetPosets
St001879: Posets ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
[3,2,1] => [[[.,.],.],.]
=> [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[4,2,1,3] => [[[.,.],[.,.]],.]
=> [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[4,2,3,1] => [[[.,.],[.,.]],.]
=> [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[4,3,2,1] => [[[[.,.],.],.],.]
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[5,2,1,3,4] => [[[.,.],[.,[.,.]]],.]
=> [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,2,1,4,3] => [[[.,.],[[.,.],.]],.]
=> [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
[5,2,3,1,4] => [[[.,.],[.,[.,.]]],.]
=> [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,2,3,4,1] => [[[.,.],[.,[.,.]]],.]
=> [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,2,4,1,3] => [[[.,.],[[.,.],.]],.]
=> [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
[5,2,4,3,1] => [[[.,.],[[.,.],.]],.]
=> [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
[5,3,2,1,4] => [[[[.,.],.],[.,.]],.]
=> [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[5,3,2,4,1] => [[[[.,.],.],[.,.]],.]
=> [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[5,3,4,2,1] => [[[[.,.],.],[.,.]],.]
=> [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[5,4,2,1,3] => [[[[.,.],[.,.]],.],.]
=> [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[5,4,2,3,1] => [[[[.,.],[.,.]],.],.]
=> [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[5,4,3,2,1] => [[[[[.,.],.],.],.],.]
=> [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[6,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],.]
=> [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,2,1,3,5,4] => [[[.,.],[.,[[.,.],.]]],.]
=> [1,4,5,3,2,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 12
[6,2,1,4,3,5] => [[[.,.],[[.,.],[.,.]]],.]
=> [1,3,5,4,2,6] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 10
[6,2,1,4,5,3] => [[[.,.],[[.,.],[.,.]]],.]
=> [1,3,5,4,2,6] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 10
[6,2,1,5,3,4] => [[[.,.],[[.,[.,.]],.]],.]
=> [1,4,3,5,2,6] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 10
[6,2,1,5,4,3] => [[[.,.],[[[.,.],.],.]],.]
=> [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 8
[6,2,3,1,4,5] => [[[.,.],[.,[.,[.,.]]]],.]
=> [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,2,3,1,5,4] => [[[.,.],[.,[[.,.],.]]],.]
=> [1,4,5,3,2,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 12
[6,2,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],.]
=> [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.]
=> [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,2,3,5,1,4] => [[[.,.],[.,[[.,.],.]]],.]
=> [1,4,5,3,2,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 12
[6,2,3,5,4,1] => [[[.,.],[.,[[.,.],.]]],.]
=> [1,4,5,3,2,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 12
[6,2,4,1,3,5] => [[[.,.],[[.,.],[.,.]]],.]
=> [1,3,5,4,2,6] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 10
[6,2,4,1,5,3] => [[[.,.],[[.,.],[.,.]]],.]
=> [1,3,5,4,2,6] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 10
[6,2,4,3,1,5] => [[[.,.],[[.,.],[.,.]]],.]
=> [1,3,5,4,2,6] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 10
[6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.]
=> [1,3,5,4,2,6] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 10
[6,2,4,5,1,3] => [[[.,.],[[.,.],[.,.]]],.]
=> [1,3,5,4,2,6] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 10
[6,2,4,5,3,1] => [[[.,.],[[.,.],[.,.]]],.]
=> [1,3,5,4,2,6] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 10
[6,2,5,1,3,4] => [[[.,.],[[.,[.,.]],.]],.]
=> [1,4,3,5,2,6] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 10
[6,2,5,1,4,3] => [[[.,.],[[[.,.],.],.]],.]
=> [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 8
[6,2,5,3,1,4] => [[[.,.],[[.,[.,.]],.]],.]
=> [1,4,3,5,2,6] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 10
[6,2,5,3,4,1] => [[[.,.],[[.,[.,.]],.]],.]
=> [1,4,3,5,2,6] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 10
[6,2,5,4,1,3] => [[[.,.],[[[.,.],.],.]],.]
=> [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 8
[6,2,5,4,3,1] => [[[.,.],[[[.,.],.],.]],.]
=> [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 8
[6,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],.]
=> [1,2,5,4,3,6] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> 10
[6,3,2,1,5,4] => [[[[.,.],.],[[.,.],.]],.]
=> [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 7
[6,3,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],.]
=> [1,2,5,4,3,6] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> 10
[6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.]
=> [1,2,5,4,3,6] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> 10
[6,3,2,5,1,4] => [[[[.,.],.],[[.,.],.]],.]
=> [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 7
[6,3,2,5,4,1] => [[[[.,.],.],[[.,.],.]],.]
=> [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 7
[6,3,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],.]
=> [1,2,5,4,3,6] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> 10
[6,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],.]
=> [1,2,5,4,3,6] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> 10
[6,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],.]
=> [1,2,5,4,3,6] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> 10
[6,3,5,2,1,4] => [[[[.,.],.],[[.,.],.]],.]
=> [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 7
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.