[seqfan] A248869 trees count
user42_kevin at yahoo.com.au
Sat Sep 1 11:21:26 CEST 2018
>From trying some code, it looks like A248869 counts how many rooted
unlabelled trees have isomorphic sibling subtrees in sets of at most 2.
So a vertex can have 1 sibling of the same (isomorphic) subtree, but no
more than that. (Reckoning root at the top, and "subtree" as the vertex
and everything below.)
Is there a name for trees with limited symmetry like this? Is there a
name for their automorphism groups?
Tree automorphism groups as usual are symmetric group S(n) in direct
products, and wreath products TreeGroup wr S(n) when nesting. With n<=2
for A248869, they are some of the 2-groups (order 2^k). Or n<=4 should
be some of the solvable groups. If I have my jargon right ...
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