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Self-inverse signature permutation of a Catalan bijection: row 83 of A089840.
4

%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