A082353 - OEIS

A082353

Permutation of natural numbers induced by the Catalan bijection gma082353 acting on the parenthesizations encoded by A014486/A063171.

0, 1, 2, 3, 5, 6, 4, 7, 8, 12, 13, 15, 16, 19, 9, 10, 11, 17, 18, 14, 20, 21, 22, 31, 32, 34, 35, 36, 40, 41, 43, 44, 47, 52, 53, 56, 60, 23, 24, 25, 26, 27, 28, 29, 30, 45, 46, 33, 48, 49, 50, 37, 38, 39, 54, 55, 42, 57, 58, 59, 51, 61, 62, 63, 64, 87, 88, 90, 91, 92

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..69.

A. Karttunen, Gatomorphisms (with the complete Scheme source)

Index entries for signature-permutations induced by Catalan automorphisms

PROG

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

(define (gma082353! s) (cond ((not (pair? s)) s) ((not (pair? (cdr s))) s) ((not (pair? (car s))) (robr! (swap! s))) (else (robr! s))))

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

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