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

0,3

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

Prog

(Destructive version of this automorphism in Scheme:) (define (*A154123! s) (if (and (pair? s) (pair? (cdr s)) (pair? (cddr s))) (*A074679! (cdr s)) (*A089851! s)) s)

Crossrefs

Inverse: A154124. Cf. A154121.

Sequence in context: A152206 A371155 A368230 * A082353 A130343 A130381

Adjacent sequences: A154120 A154121 A154122 * A154124 A154125 A154126

Keyword

nonn

Author

Antti Karttunen, Jan 06 2009

Status

approved