[seqfan] Re: Coord. seqs., the coloring book approach; 2-uniform tilings

neil greubel jthomae at gmail.com
Wed Mar 28 16:39:25 CEST 2018


A note: it looks like the image from the top of page 8 was intended to be
on the last page in a different color scheme.  It also appears that it was
added as a separate upload file when the paper was uploaded. If it was done
this way the arXiv system then keeps them apart.

On Wed, Mar 28, 2018, 7:25 AM Neil Sloane <njasloane at gmail.com> wrote:

> Joerg,
>
> The very last page of the version on the arXiv is a mystery,
> where it says "This figure "grid2.png" is available in "png" format from:
>  http://arxiv.org/ps/1803.08530v1"  That sentence was not part of the
> original version
> that we sent to the arXiv.
>
> I have put a better version of the article (without that sentence) on my
> home
> page, and dated March 28 2018.
> See http://neilsloane.com/  and specifically
> http://neilsloane.com/doc/Cairo.pdf
>
> Re Bib entry [16]:
>  C. Goodman-Strauss and N. J. A. Sloane, A Tiling Coloring Book, 2018
>  (available from the authors).
> , you asked "Is this online somewhere?"  The answer is No.  In fact it is
> not finished.
>
>
> On Wed, Mar 28, 2018 at 6:11 AM, Joerg Arndt <arndt at jjj.de> wrote:
>
> > Sweet!
> >
> > There are two (trivial) things unclear to me:
> >
> > Bib entry [16]:
> >  C. Goodman-Strauss and N. J. A. Sloane, A Tiling Coloring Book, 2018
> >  (available from the authors).
> > Is this online somewhere?
> >
> > The very last page says
> > "This figure "grid2.png" is available in "png" format from:
> >  http://arxiv.org/ps/1803.08530v1"
> > what does "This" refer to?
> >
> > Best regards,   jj
> >
> > * Neil Sloane <njasloane at gmail.com> [Mar 28. 2018 11:26]:
> > > Dear SeqFans, Chaim Goodman-Strauss and I have written up our coloring
> > book
> > > method for finding coordination seqs, see
> > > "A Coloring Book Approach to Finding Coordination Sequences",
> > > https://arxiv.org/abs/1803.08530
> > >
> > > The motivation was to find simple proofs for various conjectured
> formulas
> > > in the OEIS (see for example A250120).
> > >
> > > The latter is one of the 11 uniform tilings, see
> > >
> > > List of coordination sequences for uniform planar nets: A008458(the
> > planar
> > > net 3.3.3.3.3.3), A008486 (6^3), A008574 (4.4.4.4 and 3.4.6.4), A008576
> > > (4.8.8), A008579 (3.6.3.6), A008706(3.3.3.4.4), A072154 (4.6.12),
> A219529
> > > (3.3.4.3.4), A250120(3.3.3.3.6), A250122 (3.12.12).
> > > These now all have g.f.s.
> > >
> > > I've just added all 20 2-uniform tilings to the OEIS, see
> > >
> > > Coordination sequences for the 20 2-uniform tilings in the order in
> which
> > > they appear in the Galebach catalog, together with their names in the
> > RCSR
> > > database (two sequences per tiling): #1 krt A265035, A265036; #2 cph
> > > A301287, A301289; #3 krm A301291, A301293; #4 krl A301298, A298024; #5
> > krq
> > > A301299, A301301; #6 krs A301674, A301676; #7 krr A301670, A301672; #8
> > krk
> > > A301291, A301293; #9 krn A301678, A301680; #10 krg A301682, A361684;
> #11
> > > bew A008574, A296910; #12 krh A301686, A301688; #13 krf A301690,
> A301692;
> > > #14 krd A301694, A219529; #15 krc A301708, A301710; #16 usm A301712,
> > > A301714; #17 krj A219529, A301697; #18 krc A301716, A301718; #19 krb
> > > A301720, A301722; #20 kra A301724, A301726.
> > >
> > > Many of these have only the 10 terms that RCSR gives.  If anyone has
> > access
> > > to ToposPro, that will give 127 terms (the program is free but
> requires a
> > > Windows machine).  If we had more terms we could then probably guess a
> > g.f.
> > > using gfun.
> > >
> > > Even without more terms, our coloring book method should easily produce
> > > recurrences in most cases, if anyone wants to try it. It is also great
> > fun
> > > to play with - we were originally going to call the paper "A Child's
> > > Coloring Book Approach to Finding Coordination Sequences". But children
> > are
> > > not essential, all you need are colored pencils.
> > >
> > > --
> > > Seqfan Mailing list - http://list.seqfan.eu/
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>


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