|
Search: id:A156946
|
|
|
| A156946 |
|
Geodesic growth sequence for Richard Thompson's group F with the standard generating set x_0,x_1. |
|
+0
1
|
|
| 1, 4, 12, 36, 108, 324, 952, 2800, 8132, 23608, 67884, 195132, 556932, 1588836, 4507524, 12782560, 36088224, 101845032, 286372148, 804930196, 2255624360, 6318588308, 17654567968
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
a(n) is the number of geodesics of length n in the Cayley graph of Richard Thompson's group F with the standard generating set {x_0,x_1}.
|
|
REFERENCES
|
M. Elder, E. Fusy and A. Rechnitzer, Counting elements and geodesics in Thompson's group $F$. Arxiv: 0902.0202
R.Grigorchuk and T. Smirnova-Nagnibeda, Complete growth functions of hyperbolic groups. Inven. Math. 130(1):159--188, 1997.
|
|
LINKS
|
M. Elder, E. Fusy and A. Rechnitzer, Counting elements and geodesics in Thompson's group $F$
|
|
EXAMPLE
|
For n=6 there are a(6)=952 geodesics of length 6 - there are 4.3^5=972 reduced words in the letters x_0, x_0^{-1}, x_1, x_1^{-1}, and the shortest relation in $F$ has length 10.
|
|
CROSSREFS
|
Cf. A156945, the number of elements in $F$.
Sequence in context: A006817 A003119 A001394 this_sequence A003946 A052156 A000781
Adjacent sequences: A156943 A156944 A156945 this_sequence A156947 A156948 A156949
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Murray Elder (murrayelder(AT)gmail.com), Feb 19 2009
|
|
|
Search completed in 0.002 seconds
|
