cp's OEIS Frontend

Row n is the signature permutation of the Catalan automorphism which is obtained from the n-th automorphism in the table A122203 with the recursion scheme "ENIPS", or equivalently row n is obtained as ENIPS(SPINE(n-th row of A089840)). See A122203 and A122204 for the description of SPINE and ENIPS. Each row occurs only once in this table. Inverses of these permutations can be found in table A122286. This table contains also all the rows of A122204 and A089840.

Row n is the signature permutation of the Catalan automorphism which is obtained from the n-th automorphism in the table A122204 with the recursion scheme "SPINE", or equivalently row n is obtained as SPINE(ENIPS(n-th row of A089840)). See A122203 and A122204 for the description of SPINE and ENIPS. Each row occurs only once in this table. Inverses of these permutations can be found in table A122285. This table contains also all the rows of A122203 and A089840.

This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it returns back toward the root, after descending down to the leftmost tip of the tree along the 000... ray, so that the last vertex whose descendants are swapped, is the left-hand side child of the root and the root itself is fixed. Specifically, *A154453 = psi(A154443), where the isomorphism psi is given in A153141 (see further comments there).

This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it descends along the 000... ray, but not starting swapping until at the left-hand side child of the root, leaving the root itself fixed. Specifically, *A154454 = psi(A154444), where the isomorphism psi is given in A153141 (see further comments there).