cp's OEIS Frontend

Row n is the signature permutation of the Catalan automorphism which is obtained from the n-th nonrecursive automorphism in the table A089840 with the recursion scheme "FORK". In this recursion scheme the given automorphism is first applied at the root of binary tree, before the algorithm recurses down to the both branches (new ones, possibly changed by the given automorphism). I.e. this corresponds to the pre-order (prefix) traversal of a Catalan structure, when it is interpreted as a binary tree. The associated Scheme-procedures FORK and !FORK can be used to obtain such a transformed automorphism from any constructively or destructively implemented automorphism. Each row occurs only once in this table. Inverses of these permutations can be found in table A122202.

Row n is the signature permutation of the Catalan automorphism which is obtained from the n-th nonrecursive automorphism in the table A089840 with the recursion scheme "INORDER". In this recursion scheme the given automorphism is applied at the root of binary tree after the algorithm has recursed down the car-branch (the left hand side tree in the context of binary trees), but before the algorithm recurses down to the cdr-branch (the right hand side of the binary tree, with respect to the new orientation of branches, possibly changed by the applied automorphism). I.e. this corresponds to the depth-first in-order traversal of a Catalan structure, when it is interpreted as a binary tree. The associated Scheme-procedures INORDER and !INORDER can be used to obtain such a transformed automorphism from any constructively (or respectively: destructively) implemented automorphism. Each row occurs only once in this table and similar notes as given e.g. for table A122202 apply here, e.g. the rows of A089840 all occur here as well. This transformation has many fixed points besides the trivial identity automorphism *A001477: at least *A069770, *A089863 and *A129604 stay as they are. Inverses of these permutations can be found in table A130401.

The signature-permutation of the automorphism which is derived from the third non-recursive automorphism *A089850 with recursion schema KROF (see A122202 for the definition).