Identifier
-
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
St000501: Permutations ⟶ ℤ
Values
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>1
[.,[.,.]]=>[2,1]=>2
[[.,.],.]=>[1,2]=>1
[.,[.,[.,.]]]=>[3,2,1]=>3
[.,[[.,.],.]]=>[2,3,1]=>3
[[.,.],[.,.]]=>[1,3,2]=>1
[[.,[.,.]],.]=>[2,1,3]=>2
[[[.,.],.],.]=>[1,2,3]=>1
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>4
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>4
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>4
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>4
[.,[[[.,.],.],.]]=>[2,3,4,1]=>4
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>1
[[.,.],[[.,.],.]]=>[1,3,4,2]=>1
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>2
[[[.,.],.],[.,.]]=>[1,2,4,3]=>1
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>3
[[.,[[.,.],.]],.]=>[2,3,1,4]=>3
[[[.,.],[.,.]],.]=>[1,3,2,4]=>1
[[[.,[.,.]],.],.]=>[2,1,3,4]=>2
[[[[.,.],.],.],.]=>[1,2,3,4]=>1
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>5
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>5
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>5
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>5
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>5
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>5
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>5
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>5
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>5
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>5
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>5
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>5
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>5
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>5
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>1
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>1
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>1
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>1
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>1
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>2
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>2
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>1
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>1
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>3
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>3
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>1
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>2
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>1
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>4
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>4
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>4
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>4
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>4
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>1
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>1
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>2
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>1
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>3
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>3
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>1
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>2
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>1
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>6
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>6
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>6
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>6
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>6
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>6
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>6
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>6
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>6
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>6
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>6
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>6
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>6
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>6
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>6
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>6
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>6
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>6
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>6
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>6
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>6
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>6
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>6
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>6
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>6
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>6
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>6
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>6
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>6
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>6
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>6
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>6
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>6
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>6
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>6
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>6
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>6
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>6
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>6
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>6
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>6
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>6
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>1
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>1
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>1
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>1
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>1
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>1
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>1
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>1
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>1
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>1
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>1
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>1
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>1
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>1
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>2
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>2
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>2
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>2
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>2
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>1
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>1
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>1
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>1
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>1
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>3
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>3
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>3
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>3
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>1
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>1
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>2
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>2
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>1
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>1
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>4
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>4
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>4
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>4
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>4
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>1
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>1
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>2
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>1
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>3
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>3
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>1
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>2
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>1
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>5
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>5
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>5
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>5
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>5
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>5
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>5
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>5
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>5
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>5
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>5
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>5
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>5
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>5
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>1
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>1
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>1
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>1
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>1
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>2
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>2
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>1
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>1
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>3
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>3
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>1
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>2
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>1
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>4
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>4
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>4
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>4
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>4
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>1
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>1
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>2
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>1
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>3
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>3
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>1
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>2
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>1
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>1
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>1
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>1
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>1
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>1
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>1
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>1
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>1
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>1
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>1
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>1
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>1
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>1
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>1
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>1
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>1
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>1
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>1
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>1
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>1
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>1
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>1
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>1
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>1
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>1
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>1
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>1
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>1
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>1
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>1
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>1
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>1
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>1
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>1
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>1
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>1
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>1
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>1
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>1
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>1
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>1
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>1
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>1
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>1
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>1
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>1
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>1
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>1
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>1
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>1
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>1
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>1
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>1
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>1
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>1
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>1
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>1
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>1
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>1
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>1
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>1
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>1
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>1
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>1
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>1
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>1
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>1
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>1
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>1
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>1
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>1
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>1
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>1
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>1
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>1
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>1
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>1
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>1
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>1
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>1
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>1
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>1
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>1
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>1
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>1
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>1
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>1
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>1
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>1
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>1
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>1
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>1
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>1
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>1
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>1
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>1
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>1
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>1
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>1
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>1
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>1
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>1
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>1
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>1
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>1
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>1
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>1
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>1
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>1
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Description
The size of the first part in the decomposition of a permutation.
For a permutation $\pi$ of $\{1,\ldots,n\}$, this is defined to be the smallest $k > 0$ such that $\{\pi(1),\ldots,\pi(k)\} = \{1,\ldots,k\}$. This statistic is undefined for the empty permutation.
For the number of parts in the decomposition see St000056The decomposition (or block) number of a permutation..
For a permutation $\pi$ of $\{1,\ldots,n\}$, this is defined to be the smallest $k > 0$ such that $\{\pi(1),\ldots,\pi(k)\} = \{1,\ldots,k\}$. This statistic is undefined for the empty permutation.
For the number of parts in the decomposition see St000056The decomposition (or block) number of a permutation..
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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