A154121 Signature permutation of a Catalan bijection: row 3655 of A089840.

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

Offset

0,3

Comments

This bijection of binary trees can be obtained by applying bijection *A074679 to the right hand side subtree and leaving the left hand side subtree intact:

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

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

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

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

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

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

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

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

Note that the first clause corresponds to generator B of Thompson's groups F, T and V, while *A074679's first clause corresponds to generator A and furthermore, *A089851 corresponds to generator C and *A072796 to generator pi_0 of Thompson's group V. (To be checked: can Thompson's V be embedded in A089840 by using these or some other suitably chosen generators?)

Comment to above: I think now that it is a misplaced hope to embed V in A089840. Instead, it is more probable that Thompson's V is isomorphic to the quotient group A089840/N, where N is a subgroup of A089840 which includes identity (*A001477) and any other bijection (e.g. *A154126) that fixes all large enough trees. For more details, see my "On the connection of A089840 with ..." page. - Antti Karttunen, Aug 23 2012

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.

A. Karttunen, On the connection of A089840 with Thompson's groups, speculation and conjectures.

Index entries for signature-permutations of Catalan automorphisms

Prog

(Scheme)
;; Destructive version of this automorphism:
(define (*A154121! s) (if (pair? s) (*A074679! (cdr s))) s)

Crossrefs

Inverse: A154122. a(n) = A069770(A089865(A069770(n))). Cf. A154123, A154126.

Sequence in context: A060119 A060126 A216250 * A130375 A154122 A089850

Adjacent sequences: A154118 A154119 A154120 * A154122 A154123 A154124

Keyword

nonn

Author

Antti Karttunen, Jan 06 2009

Status

approved