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The signature-permutation of the automorphism which is derived from the second non-recursive automorphism *A072796 either with recursion schema DEEPEN or NEPEED. (see A122283, A122284 for their definitions).

This automorphism is illustrated below, where letters A, B, C, D, E and F refer to arbitrary subtrees located on those nodes and () stands for an implied terminal node.

.............................B...C............F...B......

..............................\./..............\./.......

...............................x...D............x...C....

................................\./..............\./.....

.................................x...E............x...D..

..................................\./.....-->......\./...

..A...B.........C...A..............x...F............x...E

...\./...........\./................\./..............\./.

....x...C...-->...x...B..........()..x............()..x..

.....\./...........\./............\./..............\./...

......x.............x..............x................x....

This is the last multiclause automorphism of total seven opened conses in the table A089840. The next nonrecursive automorphism, A089840[1786786], which consists of a single seven-node clause, swaps the first two toplevel elements (of a general plane tree, like *A072796 does), but only if A057515(n) > 6 and in other cases keeps the tree intact.

This involution effects the following transformation on the binary trees (labels A,B,C,D refer to arbitrary subtrees located on those nodes and () stands for a terminal node.)

.....C...D.........A...D

......\./...........\./

...B...X2........C...Y2......B..().......A..()

....\./...........\./.........\./.........\./

.A...X1....-->.B...Y1......A...X1..-->.B...Y1

..\./...........\./.........\./.........\./

...X0............Y0..........X0..........Y0

Note that automorphism *A072796 = SPINE(*A129605). See the definition given in A122203.

This involution effects the following transformation on the binary trees (labels A,B,C,D refer to arbitrary subtrees located on those nodes and () stands for a terminal node.)

.....C...D.........B...D

......\./...........\./

...B...X2........A...Y2......B..().......A..()

....\./...........\./.........\./.........\./

.A...X1....-->.C...Y1......A...X1..-->.B...Y1

..\./...........\./.........\./.........\./

...X0............Y0..........X0..........Y0

Note that automorphism *A072796 = ENIPS(*A129606). See the definition given in A122204.

Otherwise like automorphism *A072796, except that this involution exchanges the two leftmost subtrees of a general tree ONLY when the degree of the tree is two. Automorphism *A129608 = SPINE(*A129607) = ENIPS(*A129607). See the definitions given in A122203 and A122204.

This is a self-inverse automorfism (an involution). Can be used to construct A130373.

The signature-permutation of the automorphism which is derived from the second non-recursive automorphism *A072796 with FORK(FORK(*A072796)) = FORK(*A057511). (see A122201 for the definition of FORK).

The signature-permutation of the automorphism which is derived from the second non-recursive automorphism *A072796 with KROF(KROF(*A072796)) = KROF(*A057512). (see A122202 for the definition of KROF).

This self-inverse automorphism permutes the top level of a list of even length (1 2 3 4 ... 2n-1 2n) as (2 1 4 3 ... 2n 2n-1), and when applied to a list of odd length (1 2 3 4 ... 2n-1 2n 2n+1), permutes it as (2 1 4 3 ... 2n 2n-1 2n+1).