A154123 Signature permutation of a Catalan bijection: row 3656 of A089840.

0, 1, 2, 3, 5, 6, 4, 7, 8, 11, 12, 13, 16, 19, 15, 14, 9, 17, 18, 10, 20, 21, 22, 28, 29, 30, 31, 32, 33, 34, 35, 44, 47, 36, 53, 56, 60, 39, 40, 41, 42, 51, 43, 37, 23, 45, 46, 24, 48, 49, 50, 52, 38, 25, 54, 55, 26, 57, 58, 59, 27, 61, 62, 63, 64, 79, 80, 81, 82, 83, 84, 85

Offset: 0

Author

Antti Karttunen, Jan 06 2009

Keywords

• nonn

Comments

This bijection of binary trees is obtained in the following way. See also comments at A154122.

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

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

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

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

A...x...........A...x.................A...x.........B...x....

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

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

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

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

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

Note that the first clause corresponds to generator B of Thompson's groups F, T and V. See further comments at A154121.

Links

• A. Karttunen, Table of n, a(n) for n = 0..2055
• J. W. Cannon, W. J. Floyd, and W. R. Parry, Notes on Richard Thompson's Groups F and T
• J. W. Cannon, W. J. Floyd, and W. R. Parry, Introductory notes on Richard Thompson's groups, L'Enseignement Mathématique, Vol. 42 (1996), pp. 215-256.
• Index entries for signature-permutations of Catalan automorphisms

Crossrefs

Inverse: A154124. Cf. A154121.