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

Author

Murray Elder, Sep 06 2014

Keywords

• nonn
• hard

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.

Examples

			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.
		

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