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.
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 06 2009
STATUS
approved