|
%I #5 Mar 31 2012 13:21:17
%S 0,1,2,3,5,4,6,7,8,12,13,9,10,11,15,14,16,17,18,19,20,21,22,31,32,34,
%T 35,36,23,24,25,26,27,28,29,30,33,40,41,37,38,39,43,42,44,45,46,47,48,
%U 49,50,52,51,53,54,55,56,57,58,59,60,61,62,63,64,87,88,90,91,92,96,97
%N Signature permutation of a Catalan bijection: row 3747 of A089840.
%C This bijection of binary trees can be obtained by applying bijection *A074680 to the right hand side subtree and leaving the left hand side subtree intact. See also comments at A154121.
%C .B...C...............C...D
%C ..\./.................\./
%C ...x...D....-->....B...x.................()..C ........C...()
%C ....\./.............\./...................\./....-->....\./...
%C .A...x...........A...x.................A...x.........A...x....
%C ..\./.............\./...................\./...........\./.....
%C ...x...............x.....................x.............x......
%C ..............................................................
%C That is, (a . ((b . c) . d)) -> (a . (b . (c . d)))
%C or (a . (() . c)) -> (a . (c . ())) if the former is not possible.
%H A. Karttunen, <a href="/A154122/b154122.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 (*A154122! s) (if (pair? s) (*A074680! (cdr s))) s)
%Y Inverse: A154121. a(n) = A069770(A089866(A069770(n))). Cf. A154124.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 06 2009
|
