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 A154124 Signature permutation of a Catalan bijection: row 3748 of A089840. 4

%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 signature-permutations 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

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Last modified December 15 17:03 EST 2019. Contains 330000 sequences. (Running on oeis4.)