0,3

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.

A. Karttunen, Table of n, a(n) for n = 0..2055

A. Karttunen, Prolog-program which illustrates the construction of this and similar nonrecursive Catalan automorphisms.

Index entries for signature-permutations of Catalan automorphisms

(Constructive and destructive Scheme implementation of this automorphism. These act on S-expressions, i.e. list-structures:)

(define (*A129606 s) (cond ((> (length s) 2) (cons (caddr s) (cons (car s) (cons (cadr s) (cdddr s))))) (else (*A072796 s))))

(define (*A129606! s) (cond ((< (length s) 3) (*A072796! s)) (else (let ((org_car (car s))) (set-car! s (caddr s)) (set-car! (cddr s) (cadr s)) (set-car! (cdr s) org_car) s))))

Inverse: A129605.

Sequence in context: A057511 A121730 A062894 this_sequence A057510 A130920 A127285

Adjacent sequences: A129603 A129604 A129605 this_sequence A129607 A129608 A129609

nonn

Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), May 22 2007