[seqfan] Re: Fwd: Worry about old sequence, A030077, paths in K_n, and new sequence A352568

Brendan McKay Brendan.McKay at anu.edu.au
Sun Apr 3 16:58:35 CEST 2022

On page 2 of that paper it says "Horak and Rosa generalize this to 
composite v and show that the condition on divisors is necessary".

Doesn't this mean that every realizable multiset is admissible? Don't 
trust me on that.

One more thing before I go to bed: this gives a way of extending A030077 
up to 19 as well, since it is only necessary to compare the lengths of 
the admissible multisets which are vastly fewer than the number of paths.


On 4/4/2022 12:42 am, D. S. McNeil wrote:
> Unfortunately there's a gap, realized (naturally) as soon as I hit 
> send: while we have that every admissible multiset up to v=19 is 
> realizable, I don't think we have that every realizable multiset needs 
> to be admissible.  Without that, all we have is a lower bound, and not 
> known values.
> Doug

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