login
Number of equivalence classes of words in F_2, modulo all automorphisms of F_2, whose minimal words have length n.
1

%I #10 Oct 03 2016 12:36:31

%S 1,1,1,1,3,4,10,16,43,101,340,911,2544,7224,22616,65376,187754,545743,

%T 1653966,4832057,14027794

%N Number of equivalence classes of words in F_2, modulo all automorphisms of F_2, whose minimal words have length n.

%C F_2 is the free group on two generators.

%H Bobbe Cooper and Eric Rowland, <a href="http://arxiv.org/abs/0909.0561">Growing words in the free group on two generators</a>, Illinois Journal of Mathematics 55 (2011) 417-426.

%H Bobbe Cooper and Eric Rowland, <a href="https://arxiv.org/abs/1307.8216">Classification of automorphic conjugacy classes in the free group on two generators</a>, Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography, edited by Delaram Kahrobaei and Vladimir Shpilrain, Contemporary Mathematics 633 (2015) 13-40.

%Y A224074 is the number of root classes.

%K nonn,hard

%O 0,5

%A _Eric Rowland_, Mar 30 2013