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A154125 Self-inverse signature permutation of a Catalan bijection: row 83 of A089840. 3
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, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 44, 47, 53, 56, 60, 42, 51, 37, 45, 46, 38, 48, 49, 50, 43, 52, 39, 54, 55, 40, 57, 58, 59, 41, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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.

.A...B.C...D.......C...D.A...B.

..\./...\./.........\./...\./..

...x.....x...--->....x.....x...

....\.../.............\.../....

......x.................x......

...............................

((a . b) . (c . d)) -> ((c . d) . (a . b))

or fix, if either the left or right hand side subtree is empty.

LINKS

A. Karttunen, Table of n, a(n) for n = 0..2055

Index entries for signature-permutations of Catalan automorphisms

PROG

(Destructive version of this automorphism in Scheme:) (define (*A154125! s) (if (and (pair? s) (pair? (car s)) (pair? (cdr s))) (*A069770! s)) s)

CROSSREFS

Inverse: A154125. a(n) = A069770(A154126(n)) = A154126(A069770(n)).

Sequence in context: A283657 A053432 A261888 * A106039 A151767 A213517

Adjacent sequences:  A154122 A154123 A154124 * A154126 A154127 A154128

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 06 2009

STATUS

approved

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Last modified October 22 03:04 EDT 2019. Contains 328315 sequences. (Running on oeis4.)