[seqfan] Re: Fwd: Worry about old sequence, A030077, paths in K_n, and new sequence A352568
njasloane at gmail.com
Sun Apr 3 16:35:39 CEST 2022
Doug, Could you log in and update A352568 accordingly? Thanks!
Neil J. A. Sloane, Chairman, OEIS Foundation.
Also Visiting Scientist, Math. Dept., Rutgers University,
Email: njasloane at gmail.com
On Sun, Apr 3, 2022 at 10:28 AM D. S. McNeil <dsm054 at gmail.com> wrote:
> 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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