Identifier
-
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00223: Permutations —runsort⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤ
Values
=>
Cc0010;cc-rep-0
Cc0014;cc-rep
[.,[.,[.,.]]]=>[3,2,1]=>[1,2,3]=>([(0,2),(2,1)],3)=>3
[.,[[.,.],.]]=>[2,3,1]=>[1,2,3]=>([(0,2),(2,1)],3)=>3
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>([(0,2),(2,1)],3)=>3
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>6
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>6
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>6
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>6
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>5
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[1,2,4,5,3,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>5
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>5
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>6
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>4
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[1,4,5,2,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>4
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[1,3,5,2,4,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>6
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>5
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>4
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>5
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[1,3,4,5,2,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>4
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[1,4,5,2,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>4
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[1,2,4,5,3,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>5
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>4
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>4
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[1,3,5,2,4,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>6
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[1,3,4,2,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>5
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>5
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>6
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>7
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>7
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>7
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>7
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>6
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>6
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>6
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>7
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>5
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>5
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>7
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>6
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>5
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>6
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[1,2,4,5,6,3,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>5
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>5
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>6
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>5
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>5
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>7
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>6
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>6
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>7
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>4
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>4
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>6
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>5
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>6
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[1,4,5,6,2,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>4
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[1,3,5,6,2,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>6
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[1,3,4,6,2,5,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>6
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>5
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>7
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>6
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>4
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>4
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>6
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>5
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>5
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>5
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>7
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>6
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>4
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>4
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>6
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>6
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[1,3,4,5,6,2,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>4
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[1,4,5,6,2,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>4
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[1,2,4,5,6,3,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>5
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>4
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>4
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[1,3,5,6,2,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>6
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>6
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>4
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>4
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>4
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>4
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>4
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>6
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>6
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>7
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[1,3,4,6,2,5,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>6
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[1,3,4,5,2,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>5
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>5
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>6
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>5
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>5
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>7
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>6
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>6
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>7
search for individual values
searching the database for the individual values of this statistic
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
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 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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