|
%I #6 Oct 15 2015 10:55:24
%S 0,1,2,3,4,5,7,8,6,9,10,11,12,13,17,18,20,21,22,14,15,16,19,23,24,25,
%T 26,27,28,29,30,31,32,33,34,35,36,45,46,48,49,50,54,55,57,58,59,61,62,
%U 63,64,37,38,39,40,41,42,43,44,47,51,52,53,56,60,65,66,67,68,69
%N Permutation of natural numbers induced by the Catalan bijection gma082352 acting on the parenthesizations encoded by A014486/A063171.
%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 (gma082352! s) (cond ((not (pair? s)) s) ((not (pair? (car s))) s) ((not (pair? (caar s))) (swap! (robr! s))) (else (robr! s))))
%o (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))
%o (define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))
%Y Inverse of A082351. a(n) = A057163(A082354(A057163(n))). Cf. also A074679-A074680, A082355-A082356, A082361-A082362.
%K nonn
%O 0,3
%A _Antti Karttunen_, Apr 17 2003
|
