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A246877 Cogrowth sequence for Richard Thompson's group F with the standard generating set x_0, x_1. 1
20, 64, 336, 1160, 5896, 24652, 117628, 531136, 2559552, 12142320, 59416808, 290915560, 1449601452, 7269071976, 36877764000, 188484835300, 972003964976, 5049059855636, 26423287218612, 139205945578944 (list; graph; refs; listen; history; text; internal format)



a(n) is the number of reduced words in {x_0,x_0^{-1},x_1,x_1^{-1}}^* of length 2*n equal to the identity in F.


Murray Elder, Table of n, a(n) for n = 5..23

M. Elder, A. Rechnitzer, T. Wong, On the cogrowth of Thompson's group F, Groups, Complexity, Cryptology 4(2) (2012), 301-320.

S. Haagerup, U. Haagerup, M. Ramirez-Solano, A computational approach to the Thompson group F, Arxiv 2014


The length of the shortest relation in the group presentation is 10, there are 20 distinct cyclic permutations of this word and its inverse, and each one is a reduced trivial word of length 2*5, so a(5)=20.


Sequence in context: A033577 A262486 A187156 * A074632 A225190 A228839

Adjacent sequences:  A246874 A246875 A246876 * A246878 A246879 A246880




Murray Elder, Sep 06 2014



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Last modified December 13 08:08 EST 2018. Contains 318082 sequences. (Running on oeis4.)