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

Author

Antti Karttunen, Jan 06 2009

Keywords

• nonn

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

Crossrefs

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