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

Neil Sloane njasloane at gmail.com
Sun Apr 3 17:10:27 CEST 2022

Brendan, Old friend (we go back at least 25 years, remember
Brendan D. McKay and E. Rogoyski, Latin squares of order ten, Electron. J.
Combinatorics, 2 (1995) ?),
can I ask you to be the editor in charge of A030077 and its offshoots?  You
know everything, and I just don't have time to do a good job.

Best regards

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 10:58 AM Brendan McKay <Brendan.McKay at anu.edu.au>

> 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.
> Brendan.
> 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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