Identifier
-
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000456: Graphs ⟶ ℤ
Values
[[.,.],.] => [1,2] => ([(0,1)],2) => ([(0,1)],2) => 1
[[.,[.,.]],.] => [2,1,3] => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 1
[[[.,.],.],.] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,2),(1,2)],3) => 1
[[.,[.,[.,.]]],.] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => ([(0,3),(1,3),(2,3)],4) => 1
[[.,[[.,.],.]],.] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 1
[[[.,.],[.,.]],.] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 1
[[[.,[.,.]],.],.] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(1,3),(2,3)],4) => 1
[[[[.,.],.],.],.] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(1,2),(2,3)],4) => 1
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 1
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 1
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 1
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 1
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 1
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 1
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 1
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 1
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 1
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 1
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[.,[[.,.],[[[.,.],.],.]]],.] => [4,5,6,2,3,1,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 1
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 1
[[.,[[[.,.],.],[[.,.],.]]],.] => [5,6,2,3,4,1,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 1
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 1
[[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 1
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 1
[[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 1
[[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 1
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Description
The monochromatic index of a connected graph.
This is the maximal number of colours such that there is a colouring of the edges where any two vertices can be joined by a monochromatic path.
For example, a circle graph other than the triangle can be coloured with at most two colours: one edge blue, all the others red.
This is the maximal number of colours such that there is a colouring of the edges where any two vertices can be joined by a monochromatic path.
For example, a circle graph other than the triangle can be coloured with at most two colours: one edge blue, all the others red.
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
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
Map
to 132-avoiding permutation
Description
Return a 132-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 maximal element of the 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 maximal element of the Sylvester class.
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