[seqfan] Re: Video of my talk is now on Vimeo

[Allan Wechsler]

I enjoyed watching the talk, after the fact. I have a thought or two
regarding Conant's dissection technique. One can generalize the procedure
that generates any particular stage of the dissection. Start with a
rectangle and pick m points along the bottom edge, and n points along the
left edge. (My proposal refers to the "unsymmetrized" version of Conant's
algorithm.) Label these m+n points from 1 to m+n, in any of the (m+n)!
possible permutations. We abandon Conant's binary subdivision procedure and
simple launch the "warp" and "weft" threads in the order specified by the
chosen labels. (We can recover Conant's construction with m = n = 2^k - 1,
and the appropriate ordering permutation.)

Now I ask: for given values of m and n, what is the *maximum* number of
regions that can be achieved by a judicious choice of launching order? What
is the *minimum*? And where does Conant's preferred launching order lie on
the spectrum of possibilities? Is it particularly fruitful of regions, or
is it particularly sterile, or is it somewhere in the middle?

The maximum and minimum region counts would make interesting sequences when
read off a table indexed by m and n. The table should probably be ordered
by m and then by n from 1 to m, eliminating cases where n > m, because the
numbers will be the same if m and n are exchanged.



On Mon, Sep 14, 2020 at 7:08 AM Ami Eldar <amiram.eldar at gmail.com> wrote:

> Thanks.
>
> This is the direct URL:
>
> https://vimeo.com/457349959
>
>
>
>
> On Mon, Sep 14, 2020 at 12:35 PM Neil Sloane <njasloane at gmail.com> wrote:
>
> > It is on vimeo.  Go to  https://vimeo.com/experimentalmathematics
> > and it is at the top left.
> >
> > (I don't see how to pinpoint it with a more precise URL)
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>