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A156946
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Geodesic growth sequence for Richard Thompson's group F with the standard generating set x_0,x_1.
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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}.
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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.
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LINKS
| M. Elder, E. Fusy and A. Rechnitzer, Counting elements and geodesics in Thompson's group $F$
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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.
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CROSSREFS
| Cf. A156945, the number of elements in $F$.
Sequence in context: A163315 A003119 A001394 * A163877 A164353 A164697
Adjacent sequences: A156943 A156944 A156945 * A156947 A156948 A156949
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KEYWORD
| nonn
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AUTHOR
| Murray Elder (murrayelder(AT)gmail.com), Feb 19 2009
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