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A156946 Geodesic growth sequence for Richard Thompson's group F with the standard generating set x_0, x_1. 0
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; text; internal format)



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}.


M. Elder, E. Fusy, A. Rechnitzer, Counting elements and geodesics in Thompson's Group F, J. Alg. 324 (2010) 102-121 doi:10.1016/j.jalgebra.2010.02.035


Table of n, a(n) for n=0..22.

M. Elder, É. 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.


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.


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




Murray Elder, Feb 19 2009



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Last modified December 16 14:52 EST 2018. Contains 318167 sequences. (Running on oeis4.)