A154124 Signature permutation of a Catalan bijection: row 3748 of A089840.

0, 1, 2, 3, 6, 4, 5, 7, 8, 16, 19, 9, 10, 11, 15, 14, 12, 17, 18, 13, 20, 21, 22, 44, 47, 53, 56, 60, 23, 24, 25, 26, 27, 28, 29, 30, 33, 43, 52, 37, 38, 39, 40, 42, 31, 45, 46, 32, 48, 49, 50, 41, 51, 34, 54, 55, 35, 57, 58, 59, 36, 61, 62, 63, 64, 128, 131, 137, 140, 144

Offset: 0

Author

Antti Karttunen, Jan 06 2009

Keywords

• nonn

Comments

This bijection of binary trees is obtained in the following way. (Inverse of Thompson's B!):

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

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

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

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

.A...x...........A...x.................A...x.........C...x....

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

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

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

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

or (a . (() . c)) -> (c . (a . ())) 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: A154123. Cf. A154122.