%I
%S 0,1,2,3,6,4,5,7,8,16,19,9,10,11,15,14,12,17,18,13,20,21,22,44,47,53,
%T 56,60,23,24,25,26,27,28,29,30,33,43,52,37,38,39,40,42,31,45,46,32,48,
%U 49,50,41,51,34,54,55,35,57,58,59,36,61,62,63,64,128,131,137,140,144
%N Signature permutation of a Catalan bijection: row 3748 of A089840.
%C This bijection of binary trees is obtained in the following way. (Inverse of Thompson's B!):
%C .B...C...............C...D
%C ..\./.................\./
%C ...x...D....>....B...x.................()..C ........A...()
%C ....\./.............\./...................\./....>....\./...
%C .A...x...........A...x.................A...x.........C...x....
%C ..\./.............\./...................\./...........\./.....
%C ...x...............x.....................x.............x......
%C ..............................................................
%C That is, (a . ((b . c) . d)) > (a . (b . (c . d)))
%C or (a . (() . c)) > (c . (a . ())) if the former is not possible.
%H A. Karttunen, <a href="/A154124/b154124.txt">Table of n, a(n) for n = 0..2055</a>
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signaturepermutations of Catalan automorphisms</a>
%o (Destructive version of this automorphism in Scheme:) (define (*A154124! s) (if (and (pair? s) (pair? (cdr s)) (pair? (cadr s))) (*A074680! (cdr s)) (*A089853! s)) s)
%Y Inverse: A154123. Cf. A154122.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 06 2009
