0,3

This "gatomorphism" rotates caar, cdar and cdr of an S-exp as ((a . b) . c) -> ((c . a) . b) if possible.

A. Karttunen, C-program for computing this sequence

Index entries for signature-permutations induced by Catalan automorphisms

(Scheme functions implementing this automorphism on list-structures:)

(define (gma089857! s) (cond ((not (pair? s)) s) ((not (pair? (car s))) s) (else (swap! s) (robl! s) s)))

(define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))

(define (robl! s) (let ((ex-car (car s))) (set-car! s (cddr s)) (set-cdr! (cdr s) ex-car) (swap! (cdr s)) (swap! s) s))

Inverse of A089855. a(n) = A074679(A069770(n)) = A069770(A089862(n)) = A057163(A089851(A057163(n))). Row 11 of A089840.

Number of cycles: A089847. Number of fixed-points: A089848. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

Sequence in context: A082351 A122319 A123714 this_sequence A122316 A130990 A131150

Adjacent sequences: A089854 A089855 A089856 this_sequence A089858 A089859 A089860

nonn

Antti Karttunen (Firstname.Surname(AT)iki.fi), Nov 29 2003