Identifier
-
Mp00061:
Permutations
—to increasing tree⟶
Binary trees
St000126: Binary trees ⟶ ℤ
Values
=>
Cc0010;cc-rep
[1]=>[.,.]=>0
[1,2]=>[.,[.,.]]=>0
[2,1]=>[[.,.],.]=>0
[1,2,3]=>[.,[.,[.,.]]]=>0
[1,3,2]=>[.,[[.,.],.]]=>0
[2,1,3]=>[[.,.],[.,.]]=>0
[2,3,1]=>[[.,[.,.]],.]=>0
[3,1,2]=>[[.,.],[.,.]]=>0
[3,2,1]=>[[[.,.],.],.]=>0
[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>0
[1,2,4,3]=>[.,[.,[[.,.],.]]]=>0
[1,3,2,4]=>[.,[[.,.],[.,.]]]=>0
[1,3,4,2]=>[.,[[.,[.,.]],.]]=>0
[1,4,2,3]=>[.,[[.,.],[.,.]]]=>0
[1,4,3,2]=>[.,[[[.,.],.],.]]=>0
[2,1,3,4]=>[[.,.],[.,[.,.]]]=>0
[2,1,4,3]=>[[.,.],[[.,.],.]]=>0
[2,3,1,4]=>[[.,[.,.]],[.,.]]=>0
[2,3,4,1]=>[[.,[.,[.,.]]],.]=>0
[2,4,1,3]=>[[.,[.,.]],[.,.]]=>0
[2,4,3,1]=>[[.,[[.,.],.]],.]=>0
[3,1,2,4]=>[[.,.],[.,[.,.]]]=>0
[3,1,4,2]=>[[.,.],[[.,.],.]]=>0
[3,2,1,4]=>[[[.,.],.],[.,.]]=>0
[3,2,4,1]=>[[[.,.],[.,.]],.]=>0
[3,4,1,2]=>[[.,[.,.]],[.,.]]=>0
[3,4,2,1]=>[[[.,[.,.]],.],.]=>0
[4,1,2,3]=>[[.,.],[.,[.,.]]]=>0
[4,1,3,2]=>[[.,.],[[.,.],.]]=>0
[4,2,1,3]=>[[[.,.],.],[.,.]]=>0
[4,2,3,1]=>[[[.,.],[.,.]],.]=>0
[4,3,1,2]=>[[[.,.],.],[.,.]]=>0
[4,3,2,1]=>[[[[.,.],.],.],.]=>0
[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>1
[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]=>0
[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]=>0
[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]]=>0
[1,2,5,3,4]=>[.,[.,[[.,.],[.,.]]]]=>0
[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]=>0
[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]=>0
[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]=>0
[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]=>0
[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]]=>0
[1,3,5,2,4]=>[.,[[.,[.,.]],[.,.]]]=>0
[1,3,5,4,2]=>[.,[[.,[[.,.],.]],.]]=>0
[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]=>0
[1,4,2,5,3]=>[.,[[.,.],[[.,.],.]]]=>0
[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]=>0
[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]=>0
[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]=>0
[1,4,5,3,2]=>[.,[[[.,[.,.]],.],.]]=>0
[1,5,2,3,4]=>[.,[[.,.],[.,[.,.]]]]=>0
[1,5,2,4,3]=>[.,[[.,.],[[.,.],.]]]=>0
[1,5,3,2,4]=>[.,[[[.,.],.],[.,.]]]=>0
[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]]=>0
[1,5,4,2,3]=>[.,[[[.,.],.],[.,.]]]=>0
[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]=>0
[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]=>0
[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]=>0
[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]=>0
[2,1,4,5,3]=>[[.,.],[[.,[.,.]],.]]=>0
[2,1,5,3,4]=>[[.,.],[[.,.],[.,.]]]=>0
[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]=>0
[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]=>0
[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]=>0
[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]=>0
[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]=>0
[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]=>0
[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]=>0
[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]=>0
[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]=>0
[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]=>0
[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]=>0
[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]]=>0
[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]=>0
[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]=>0
[2,5,1,4,3]=>[[.,[.,.]],[[.,.],.]]=>0
[2,5,3,1,4]=>[[.,[[.,.],.]],[.,.]]=>0
[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]=>0
[2,5,4,1,3]=>[[.,[[.,.],.]],[.,.]]=>0
[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]=>0
[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]=>0
[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]=>0
[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]=>0
[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]=>0
[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]=>0
[3,1,5,4,2]=>[[.,.],[[[.,.],.],.]]=>0
[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]=>0
[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]=>0
[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]=>0
[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]=>0
[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]=>0
[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]=>0
[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]=>0
[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]=>0
[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]=>0
[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]=>0
[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]=>0
[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]=>0
[3,5,1,2,4]=>[[.,[.,.]],[.,[.,.]]]=>0
[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]]=>0
[3,5,2,1,4]=>[[[.,[.,.]],.],[.,.]]=>0
[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]=>0
[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]]=>0
[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.]=>0
[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]=>0
[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]=>0
[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]=>0
[4,1,3,5,2]=>[[.,.],[[.,[.,.]],.]]=>0
[4,1,5,2,3]=>[[.,.],[[.,.],[.,.]]]=>0
[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]=>0
[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]=>0
[4,2,1,5,3]=>[[[.,.],.],[[.,.],.]]=>0
[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]=>0
[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]=>0
[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]=>0
[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]=>0
[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]=>0
[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]]=>0
[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]=>0
[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]=>0
[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]=>0
[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]=>0
[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]=>0
[4,5,1,3,2]=>[[.,[.,.]],[[.,.],.]]=>0
[4,5,2,1,3]=>[[[.,[.,.]],.],[.,.]]=>0
[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]=>0
[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]=>0
[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]=>0
[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]=>0
[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]=>0
[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]=>0
[5,1,3,4,2]=>[[.,.],[[.,[.,.]],.]]=>0
[5,1,4,2,3]=>[[.,.],[[.,.],[.,.]]]=>0
[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]=>0
[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]=>0
[5,2,1,4,3]=>[[[.,.],.],[[.,.],.]]=>0
[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]]=>0
[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]=>0
[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]]=>0
[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]=>0
[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]]=>0
[5,3,1,4,2]=>[[[.,.],.],[[.,.],.]]=>0
[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]=>0
[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]=>0
[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]=>0
[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]=>0
[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]=>0
[5,4,1,3,2]=>[[[.,.],.],[[.,.],.]]=>0
[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]]=>0
[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]=>0
[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]=>0
[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]=>0
[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>2
[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]=>1
[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]=>1
[1,2,3,5,6,4]=>[.,[.,[.,[[.,[.,.]],.]]]]=>0
[1,2,3,6,4,5]=>[.,[.,[.,[[.,.],[.,.]]]]]=>1
[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]=>0
[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]=>1
[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]]=>0
[1,2,4,5,3,6]=>[.,[.,[[.,[.,.]],[.,.]]]]=>0
[1,2,4,5,6,3]=>[.,[.,[[.,[.,[.,.]]],.]]]=>0
[1,2,4,6,3,5]=>[.,[.,[[.,[.,.]],[.,.]]]]=>0
[1,2,4,6,5,3]=>[.,[.,[[.,[[.,.],.]],.]]]=>0
[1,2,5,3,4,6]=>[.,[.,[[.,.],[.,[.,.]]]]]=>1
[1,2,5,3,6,4]=>[.,[.,[[.,.],[[.,.],.]]]]=>0
[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]]=>0
[1,2,5,4,6,3]=>[.,[.,[[[.,.],[.,.]],.]]]=>0
[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]]=>0
[1,2,5,6,4,3]=>[.,[.,[[[.,[.,.]],.],.]]]=>0
[1,2,6,3,4,5]=>[.,[.,[[.,.],[.,[.,.]]]]]=>1
[1,2,6,3,5,4]=>[.,[.,[[.,.],[[.,.],.]]]]=>0
[1,2,6,4,3,5]=>[.,[.,[[[.,.],.],[.,.]]]]=>0
[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]]=>0
[1,2,6,5,3,4]=>[.,[.,[[[.,.],.],[.,.]]]]=>0
[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]]=>0
[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>1
[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]=>0
[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]=>0
[1,3,2,5,6,4]=>[.,[[.,.],[[.,[.,.]],.]]]=>0
[1,3,2,6,4,5]=>[.,[[.,.],[[.,.],[.,.]]]]=>0
[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]]=>0
[1,3,4,2,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]]=>0
[1,3,4,2,6,5]=>[.,[[.,[.,.]],[[.,.],.]]]=>0
[1,3,4,5,2,6]=>[.,[[.,[.,[.,.]]],[.,.]]]=>0
[1,3,4,5,6,2]=>[.,[[.,[.,[.,[.,.]]]],.]]=>0
[1,3,4,6,2,5]=>[.,[[.,[.,[.,.]]],[.,.]]]=>0
[1,3,4,6,5,2]=>[.,[[.,[.,[[.,.],.]]],.]]=>0
[1,3,5,2,4,6]=>[.,[[.,[.,.]],[.,[.,.]]]]=>0
[1,3,5,2,6,4]=>[.,[[.,[.,.]],[[.,.],.]]]=>0
[1,3,5,4,2,6]=>[.,[[.,[[.,.],.]],[.,.]]]=>0
[1,3,5,4,6,2]=>[.,[[.,[[.,.],[.,.]]],.]]=>0
[1,3,5,6,2,4]=>[.,[[.,[.,[.,.]]],[.,.]]]=>0
[1,3,5,6,4,2]=>[.,[[.,[[.,[.,.]],.]],.]]=>0
[1,3,6,2,4,5]=>[.,[[.,[.,.]],[.,[.,.]]]]=>0
[1,3,6,2,5,4]=>[.,[[.,[.,.]],[[.,.],.]]]=>0
[1,3,6,4,2,5]=>[.,[[.,[[.,.],.]],[.,.]]]=>0
[1,3,6,4,5,2]=>[.,[[.,[[.,.],[.,.]]],.]]=>0
[1,3,6,5,2,4]=>[.,[[.,[[.,.],.]],[.,.]]]=>0
[1,3,6,5,4,2]=>[.,[[.,[[[.,.],.],.]],.]]=>0
[1,4,2,3,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>1
[1,4,2,3,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]=>0
[1,4,2,5,3,6]=>[.,[[.,.],[[.,.],[.,.]]]]=>0
[1,4,2,5,6,3]=>[.,[[.,.],[[.,[.,.]],.]]]=>0
[1,4,2,6,3,5]=>[.,[[.,.],[[.,.],[.,.]]]]=>0
[1,4,2,6,5,3]=>[.,[[.,.],[[[.,.],.],.]]]=>0
[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]=>0
[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]]=>0
[1,4,3,5,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]=>0
[1,4,3,5,6,2]=>[.,[[[.,.],[.,[.,.]]],.]]=>0
[1,4,3,6,2,5]=>[.,[[[.,.],[.,.]],[.,.]]]=>0
[1,4,3,6,5,2]=>[.,[[[.,.],[[.,.],.]],.]]=>0
[1,4,5,2,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]]=>0
[1,4,5,2,6,3]=>[.,[[.,[.,.]],[[.,.],.]]]=>0
[1,4,5,3,2,6]=>[.,[[[.,[.,.]],.],[.,.]]]=>0
[1,4,5,3,6,2]=>[.,[[[.,[.,.]],[.,.]],.]]=>0
[1,4,5,6,2,3]=>[.,[[.,[.,[.,.]]],[.,.]]]=>0
[1,4,5,6,3,2]=>[.,[[[.,[.,[.,.]]],.],.]]=>0
[1,4,6,2,3,5]=>[.,[[.,[.,.]],[.,[.,.]]]]=>0
[1,4,6,2,5,3]=>[.,[[.,[.,.]],[[.,.],.]]]=>0
[1,4,6,3,2,5]=>[.,[[[.,[.,.]],.],[.,.]]]=>0
[1,4,6,3,5,2]=>[.,[[[.,[.,.]],[.,.]],.]]=>0
[1,4,6,5,2,3]=>[.,[[.,[[.,.],.]],[.,.]]]=>0
[1,4,6,5,3,2]=>[.,[[[.,[[.,.],.]],.],.]]=>0
[1,5,2,3,4,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>1
[1,5,2,3,6,4]=>[.,[[.,.],[.,[[.,.],.]]]]=>0
[1,5,2,4,3,6]=>[.,[[.,.],[[.,.],[.,.]]]]=>0
[1,5,2,4,6,3]=>[.,[[.,.],[[.,[.,.]],.]]]=>0
[1,5,2,6,3,4]=>[.,[[.,.],[[.,.],[.,.]]]]=>0
[1,5,2,6,4,3]=>[.,[[.,.],[[[.,.],.],.]]]=>0
[1,5,3,2,4,6]=>[.,[[[.,.],.],[.,[.,.]]]]=>0
[1,5,3,2,6,4]=>[.,[[[.,.],.],[[.,.],.]]]=>0
[1,5,3,4,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]=>0
[1,5,3,4,6,2]=>[.,[[[.,.],[.,[.,.]]],.]]=>0
[1,5,3,6,2,4]=>[.,[[[.,.],[.,.]],[.,.]]]=>0
[1,5,3,6,4,2]=>[.,[[[.,.],[[.,.],.]],.]]=>0
[1,5,4,2,3,6]=>[.,[[[.,.],.],[.,[.,.]]]]=>0
[1,5,4,2,6,3]=>[.,[[[.,.],.],[[.,.],.]]]=>0
[1,5,4,3,2,6]=>[.,[[[[.,.],.],.],[.,.]]]=>0
[1,5,4,3,6,2]=>[.,[[[[.,.],.],[.,.]],.]]=>0
[1,5,4,6,2,3]=>[.,[[[.,.],[.,.]],[.,.]]]=>0
[1,5,4,6,3,2]=>[.,[[[[.,.],[.,.]],.],.]]=>0
[1,5,6,2,3,4]=>[.,[[.,[.,.]],[.,[.,.]]]]=>0
[1,5,6,2,4,3]=>[.,[[.,[.,.]],[[.,.],.]]]=>0
[1,5,6,3,2,4]=>[.,[[[.,[.,.]],.],[.,.]]]=>0
[1,5,6,3,4,2]=>[.,[[[.,[.,.]],[.,.]],.]]=>0
[1,5,6,4,2,3]=>[.,[[[.,[.,.]],.],[.,.]]]=>0
[1,5,6,4,3,2]=>[.,[[[[.,[.,.]],.],.],.]]=>0
[1,6,2,3,4,5]=>[.,[[.,.],[.,[.,[.,.]]]]]=>1
[1,6,2,3,5,4]=>[.,[[.,.],[.,[[.,.],.]]]]=>0
[1,6,2,4,3,5]=>[.,[[.,.],[[.,.],[.,.]]]]=>0
[1,6,2,4,5,3]=>[.,[[.,.],[[.,[.,.]],.]]]=>0
[1,6,2,5,3,4]=>[.,[[.,.],[[.,.],[.,.]]]]=>0
[1,6,2,5,4,3]=>[.,[[.,.],[[[.,.],.],.]]]=>0
[1,6,3,2,4,5]=>[.,[[[.,.],.],[.,[.,.]]]]=>0
[1,6,3,2,5,4]=>[.,[[[.,.],.],[[.,.],.]]]=>0
[1,6,3,4,2,5]=>[.,[[[.,.],[.,.]],[.,.]]]=>0
[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]]=>0
[1,6,3,5,2,4]=>[.,[[[.,.],[.,.]],[.,.]]]=>0
[1,6,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],.]]=>0
[1,6,4,2,3,5]=>[.,[[[.,.],.],[.,[.,.]]]]=>0
[1,6,4,2,5,3]=>[.,[[[.,.],.],[[.,.],.]]]=>0
[1,6,4,3,2,5]=>[.,[[[[.,.],.],.],[.,.]]]=>0
[1,6,4,3,5,2]=>[.,[[[[.,.],.],[.,.]],.]]=>0
[1,6,4,5,2,3]=>[.,[[[.,.],[.,.]],[.,.]]]=>0
[1,6,4,5,3,2]=>[.,[[[[.,.],[.,.]],.],.]]=>0
[1,6,5,2,3,4]=>[.,[[[.,.],.],[.,[.,.]]]]=>0
[1,6,5,2,4,3]=>[.,[[[.,.],.],[[.,.],.]]]=>0
[1,6,5,3,2,4]=>[.,[[[[.,.],.],.],[.,.]]]=>0
[1,6,5,3,4,2]=>[.,[[[[.,.],.],[.,.]],.]]=>0
[1,6,5,4,2,3]=>[.,[[[[.,.],.],.],[.,.]]]=>0
[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]=>0
[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>1
[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>0
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[7,6,4,5,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>0
[7,6,5,1,2,3,4]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>0
[7,6,5,1,2,4,3]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>0
[7,6,5,1,3,2,4]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>0
[7,6,5,1,3,4,2]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>0
[7,6,5,1,4,2,3]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>0
[7,6,5,1,4,3,2]=>[[[[.,.],.],.],[[[.,.],.],.]]=>0
[7,6,5,2,1,3,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>0
[7,6,5,2,1,4,3]=>[[[[[.,.],.],.],.],[[.,.],.]]=>0
[7,6,5,2,3,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>0
[7,6,5,2,3,4,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>0
[7,6,5,2,4,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>0
[7,6,5,2,4,3,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>0
[7,6,5,3,1,2,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>0
[7,6,5,3,1,4,2]=>[[[[[.,.],.],.],.],[[.,.],.]]=>0
[7,6,5,3,2,1,4]=>[[[[[[.,.],.],.],.],.],[.,.]]=>0
[7,6,5,3,2,4,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>0
[7,6,5,3,4,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>0
[7,6,5,3,4,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>0
[7,6,5,4,1,2,3]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>0
[7,6,5,4,1,3,2]=>[[[[[.,.],.],.],.],[[.,.],.]]=>0
[7,6,5,4,2,1,3]=>[[[[[[.,.],.],.],.],.],[.,.]]=>0
[7,6,5,4,2,3,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>0
[7,6,5,4,3,1,2]=>[[[[[[.,.],.],.],.],.],[.,.]]=>0
[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]=>0
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Description
The number of occurrences of the contiguous pattern [.,[.,[.,[.,[.,.]]]]] in a binary tree.
oeis:A036766 counts binary trees avoiding this pattern.
oeis:A036766 counts binary trees avoiding this pattern.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
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