[seqfan] Re: Fwd: Worry about old sequence, A030077, paths in K_n, and new sequence A352568
D. S. McNeil
dsm054 at gmail.com
Sun Apr 3 16:28:40 CEST 2022
If I'm reading that literature correctly, then can't we extend the new
A352568 by a few terms, because it's known that every admissible multiset
is realizable for at least v <= 19 (in the terminology of
I think that'd give us up to
[1, 1, 1, 3, 5, 17, 28, 105, 161, 670, 1001, 4129, 6188, 26565, 38591,
167898, 245157, 1072730, 1562275]
if we simply loop over the candidate multisets and check admissibility.
On Sun, Apr 3, 2022 at 5:09 AM Brendan McKay via SeqFan <
seqfan at list.seqfan.eu> wrote:
> Thanks to a tip from Darryn Bryant, I have found that there is
> substantial literature
> related to A352568, that is
> "Take n equally spaced points on circle, connect them by a path with n-1
> line segments;
> sequence gives number of distinct multisets of segment [not path, Neil]
> The question is: Which multisets of segment lengths can be realised?
> Baratti conjectured that all multisets can be realised if n is prime.
> This is proved
> up to n=23 but remains open in general.
> Baratti, Horak and Rosa conjectured a complete answer to the the
> question and many
> special cases have been proved. Searching for these names gives many
> hits, for
> I stopped there but there are plenty more.
> Cheers, Brendan.
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