A082350 Permutation of natural numbers induced by the Catalan bijection gma082350 acting on the parenthesizations encoded by A014486/A063171.

0, 1, 3, 2, 8, 7, 4, 5, 6, 22, 21, 20, 17, 18, 9, 10, 11, 12, 13, 14, 15, 16, 19, 64, 63, 62, 58, 59, 61, 57, 54, 45, 46, 55, 48, 49, 50, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 47, 51, 52, 53, 56, 60, 196, 195, 194, 189, 190

Offset

0,3

Comments

This Catalan bijection rotates binary trees right, if possible, otherwise applies Catalan bijection A069768.

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 (gma082350! s) (cond ((pair? s) (cond ((pair? (car s)) (robr! s)) (else (gma069768! s))))) 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))

Crossrefs

Inverse of A082349. Cf. also A074679-A074680, A082335-A082336.

Number of cycles: A073193 (to be checked). Number of fixed-points: A019590. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

Sequence in context: A127292 A131165 A131158 * A082336 A122333 A130356

Adjacent sequences: A082347 A082348 A082349 * A082351 A082352 A082353

Keyword

nonn

Author

Antti Karttunen, Apr 17 2003

Status

approved