Identifier
-
Mp00072:
Permutations
—binary search tree: left to right⟶
Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤ
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
[6,3,5,2,4,1] => [[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 7
[6,3,5,4,2,1] => [[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 7
[6,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 6
[6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 6
[6,4,3,5,2,1] => [[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 6
[6,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 6
[6,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 10
[6,5,2,1,4,3] => [[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 7
[6,5,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 10
[6,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 10
[6,5,2,4,1,3] => [[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 7
[6,5,2,4,3,1] => [[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 7
[6,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 6
[6,5,3,2,4,1] => [[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 6
[6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 6
[6,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 6
[6,5,4,2,3,1] => [[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 6
[6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[7,2,1,3,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 25
[7,2,1,3,4,6,5] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 20
[7,2,1,3,5,4,6] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 17
[7,2,1,3,5,6,4] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 17
[7,2,1,3,6,4,5] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 18
[7,2,1,3,6,5,4] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7) => 15
[7,2,1,4,3,5,6] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 16
[7,2,1,4,3,6,5] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => ([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7) => 13
[7,2,1,4,5,3,6] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 16
[7,2,1,4,5,6,3] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 16
[7,2,1,4,6,3,5] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => ([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7) => 13
[7,2,1,4,6,5,3] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => ([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7) => 13
[7,2,1,5,4,3,6] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7) => 12
[7,2,1,5,4,6,3] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7) => 12
[7,2,1,5,6,4,3] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7) => 12
[7,2,1,6,3,4,5] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 17
[7,2,1,6,3,5,4] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7) => 13
[7,2,1,6,4,3,5] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => 11
[7,2,1,6,4,5,3] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => 11
[7,2,1,6,5,3,4] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7) => 12
[7,2,1,6,5,4,3] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 10
[7,2,3,1,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 25
[7,2,3,1,4,6,5] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 20
[7,2,3,1,5,4,6] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 17
[7,2,3,1,5,6,4] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 17
[7,2,3,1,6,4,5] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 18
[7,2,3,1,6,5,4] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7) => 15
[7,2,3,4,1,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 25
[7,2,3,4,1,6,5] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 20
[7,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 25
[7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 25
[7,2,3,4,6,1,5] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 20
[7,2,3,4,6,5,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 20
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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
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
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