[seqfan] Re: The gerrymandering sequence A341578 needs better explanation

[Neil Sloane]

Andrew W., Jack G.,  Thank you very much for the clarification. I have
revised A341578 accordingly.

What is the asymptotic behavior of A341578(n)?  What is the sequence of d
values?

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



On Fri, Feb 26, 2021 at 7:13 AM Andrew Weimholt <andrew.weimholt at gmail.com>
wrote:

> It's not necessarily n districts with n votes each.
>
> For n=6, it is better to gerrymander the 36 votes into 3 districts with 12
> votes each.
>
> In the former case, you'd need 15 votes to win: (4,4,4,3,0,0)
> In the latter case, you'd only need 14: (7,7,0)
>
> Andrew
>
> On Fri, Feb 26, 2021 at 3:51 AM Jack Grahl <jack.grahl at gmail.com> wrote:
>
> > I think the confusing part is the 'grid'. This has essentially nothing to
> > do with geometry.
> >
> > Given n districts, each with n votes, what is the least number of total
> > votes which allows a party to win a majority of the districts?
> >
> > The districts are winner-takes-all, and for an even number of districts,
> > it's enough to win half the districts, and tie in one further district.
> >
> > So for 5 districts of 5 votes, one party could theoretically win with 3
> > votes in each of 3 districts, and 0 in all other districts. For 8
> > districts, 5 votes in each of 4 districts, and 4 votes in a fifth
> district
> > is enough.
> >
> > On Fri, 26 Feb 2021, 10:47 Neil Sloane, <njasloane at gmail.com> wrote:
> >
> > > Typo, sorry. I meant to say:
> > >
> > > Dear Sequence Fans,  I had another look at A341578.  I accepted it
> > because
> > > some of the editors looked at it, and "gerrymandering" is an extremely
> > > important topic.  But after looking at it more closely, I admit I don't
> > > really understand the sequence.  Could someone explain the definition
> > more
> > > clearly?
> > >
> > >
> > > On Fri, Feb 26, 2021 at 4:49 AM Neil Sloane <njasloane at gmail.com>
> wrote:
> > >
> > > >
> > > > Dear Sequence Fans,  I had another look at A3415678.  I accepted it
> > > > because some of the editors looked at it, and "gerrymandering" is an
> > > > extremely important topic.  But after looking at it more closely, I
> > > admit I
> > > > don't really understand the sequence.  Could someone explain the
> > > definition
> > > > more clearly?
> > > >
> > >
> > > --
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> > >
> >
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> >
>
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