A246877 Cogrowth sequence for Richard Thompson's group F with the standard generating set x_0, x_1.

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

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

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

Adjacent sequences: A246874 A246875 A246876 * A246878 A246879 A246880

Keyword

nonn,hard

Author

Murray Elder, Sep 06 2014

Status

approved