0,3

This is the signature-permutation of Catalan automorphism which is derived from the automorphism *A123492 with the recursion schema KROF (defined in A122202). Like automorphisms *A057163 and *A069767/*A069768 these automorphisms are closed with respect to the subset of "zigzagging" binary trees (i.e. those binary trees where there are no nodes with two non-empty branches, or equivalently, those ones for which Stanley's interpretation (c) forms a non-branching line), and thus induce a permutation of binary strings. That is, starting from the root of such a binary tree, the turns taken by non-empty branches are interpreted as binary digits 0 or 1, depending on whether the tree grows to the left or right. In this manner, the Catalan automorphisms *A123494 and *A123493 induce the Binary Reflected Gray Code (see A003188 and A006068).

Index entries for signature-permutations of Catalan automorphisms

(Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define *A123494! (!KROF *A123492!))

Inverse: A123493. Row 79361 of A122202. See also A123715 and A123716.

Adjacent sequences: A123491 A123492 A123493 this_sequence A123495 A123496 A123497

Sequence in context: A123493 A123715 A082313 this_sequence A123716 A036706 A036712

nonn

Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Oct 11 2006