A154122 Signature permutation of a Catalan bijection: row 3747 of A089840.

0, 1, 2, 3, 5, 4, 6, 7, 8, 12, 13, 9, 10, 11, 15, 14, 16, 17, 18, 19, 20, 21, 22, 31, 32, 34, 35, 36, 23, 24, 25, 26, 27, 28, 29, 30, 33, 40, 41, 37, 38, 39, 43, 42, 44, 45, 46, 47, 48, 49, 50, 52, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 87, 88, 90, 91, 92, 96, 97

Offset: 0

Author

Antti Karttunen, Jan 06 2009

Keywords

• nonn

Comments

This bijection of binary trees can be obtained by applying bijection *A074680 to the right hand side subtree and leaving the left hand side subtree intact. See also comments at A154121.

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

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

...x...D....-->....B...x.................()..C ........C...()

....\./.............\./...................\./....-->....\./...

.A...x...........A...x.................A...x.........A...x....

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

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

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

That is, (a . ((b . c) . d)) -> (a . (b . (c . d)))

or (a . (() . c)) -> (a . (c . ())) if the former is not possible.

Links

• A. Karttunen, Table of n, a(n) for n = 0..2055
• Index entries for signature-permutations of Catalan automorphisms

Crossrefs

Inverse: A154121. a(n) = A069770(A089866(A069770(n))). Cf. A154124.