login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A246877
Cogrowth sequence for Richard Thompson's group F with the standard generating set x_0, x_1.
2
20, 64, 336, 1160, 5896, 24652, 117628, 531136, 2559552, 12142320, 59416808, 290915560, 1449601452, 7269071976, 36877764000, 188484835300, 972003964976, 5049059855636, 26423287218612, 139205945578944
OFFSET
5,1
COMMENTS
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.
LINKS
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
EXAMPLE
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.
CROSSREFS
Sequence in context: A033577 A262486 A187156 * A074632 A225190 A228839
KEYWORD
nonn,hard
AUTHOR
Murray Elder, Sep 06 2014
STATUS
approved