[seqfan] Re: Identifying sequence in Quanta Magazine graph theory article

[William Orrick]

Dear Bredan and Seqfans,

I received a reply from Karen Vogtmann confirming the definition of the
graphs in this enumeration and, later, a more detailed response from
Michael Borinsky informing me that the enumeration goes as high as rank 21.
I will add the numbers Michael sent me to the current draft of Andrew's new
sequence. As far as I am able to understand, the enumeration was done by
large-scaled algebraic manipulation of generating functions using code
Michael wrote in FORM. See Theorem 3.12 in the Borinsky and Vogtmann paper
for a sketch of a related computation.) This code was later highly
optimized by Jos Vermaseren. A forthcoming paper (Ref. 9 in Borinsky and
Vogtmann) will describe some of the techniques, but apparently not this
particular calculation. If anyone has looked at Borinsky and
Vogtmann's paper and can offer more insight than I am able to provide that
would be great.

-Will