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A082349 Permutation of natural numbers induced by the Catalan bijection gma082349 acting on the parenthesizations encoded by A014486/A063171. 7

%I

%S 0,1,3,2,6,7,8,5,4,14,15,16,17,18,19,20,21,12,13,22,11,10,9,37,38,39,

%T 40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,31,32,59,34,

%U 35,36,60,61,62,30,33,63,29,26,27,64,28,25,24,23,107,108,109,110,111

%N Permutation of natural numbers induced by the Catalan bijection gma082349 acting on the parenthesizations encoded by A014486/A063171.

%C This Catalan bijection rotates binary trees left, if possible, otherwise applies Catalan bijection A069767.

%H A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a> (with the complete Scheme source)

%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations induced by Catalan automorphisms</a>

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

%o (define (gma082349! s) (cond ((pair? s) (cond ((pair? (cdr s)) (robl! s)) (else (gma069767! s))))) s)

%o (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))

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

%Y Inverse of A082350. Cf. also A074679-A074680, A082335-A082336.

%Y 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).

%K nonn

%O 0,3

%A _Antti Karttunen_, Apr 17 2003

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Last modified February 21 23:44 EST 2019. Contains 320381 sequences. (Running on oeis4.)