%I #7 Dec 13 2015 17:38:25
%S 0,1,2,3,4,5,6,7,8,9,10,11,12,13,16,19,14,17,18,15,20,21,22,23,24,25,
%T 26,27,28,29,30,31,32,33,34,35,36,44,47,53,56,60,42,51,37,45,46,38,48,
%U 49,50,43,52,39,54,55,40,57,58,59,41,61,62,63,64,65,66,67,68,69,70,71
%N Self-inverse signature permutation of a Catalan bijection: row 83 of A089840.
%C This bijection of binary trees swaps the left and right subtree of a binary tree, but ONLY if BOTH are nonempty. If either the left or right hand side tree is empty, fixes the tree.
%C .A...B.C...D.......C...D.A...B.
%C ..\./...\./.........\./...\./..
%C ...x.....x...--->....x.....x...
%C ....\.../.............\.../....
%C ......x.................x......
%C ...............................
%C ((a . b) . (c . d)) -> ((c . d) . (a . b))
%C or fix, if either the left or right hand side subtree is empty.
%H A. Karttunen, <a href="/A154125/b154125.txt">Table of n, a(n) for n = 0..2055</a>
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a>
%o (Destructive version of this automorphism in Scheme:) (define (*A154125! s) (if (and (pair? s) (pair? (car s)) (pair? (cdr s))) (*A069770! s)) s)
%Y Inverse: A154125. a(n) = A069770(A154126(n)) = A154126(A069770(n)).
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 06 2009