A154125 Self-inverse signature permutation of a Catalan bijection: row 83 of A089840.

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

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: A053432 A349999 A261888 * A106039 A151767 A213517

Adjacent sequences: A154122 A154123 A154124 * A154126 A154127 A154128

Keyword

nonn

Author

Antti Karttunen, Jan 06 2009

Status

approved