[seqfan] Re: Stan Wagon's Powers of Two Problem: News!

[Max Alekseyev]

I've just uploaded a preprint describing computation of A352178(n) for n <=
18:
https://arxiv.org/abs/2303.02872

Regards,
Max

On Wed, Sep 28, 2022 at 11:39 AM Max Alekseyev <maxale at gmail.com> wrote:

> Neil et al.,
>
> In case anyone is interested, I have computed minimal forbidden subgraphs
> (MFS) of order up to 10 for graphs appearing in https://oeis.org/A352178
> An MFS is a graph that is not admissible/soluble (in the sense of A352178)
> but every its smaller subgraph is.
>
> The smallest MFS is the cycle C_4 as proved by M. S. Smith. One more MFS
> on 7 nodes is given in M. Bolan's memo (the "saw" formed by 3 triangles).
> The other graph on 10 nodes with 16 edges ("graph A") that Bolan proves
> insoluble happens to contain an MFS with 14 edges. In other words, it is
> possible to remove 2 edges from graph A so that it will still be insoluble.
>
> I've established that there exists one more MFS on 7 nodes with 9 edges
> (also formed by 3 triangles), none on 8 or 9 nodes, and 15 MFSes on 10
> nodes (1 with 13 edges, 11 with 14 edges, and 3 with 15 edges).
>
> Drawing of these MFSes can be seen at Sagecell:
> https://sagecell.sagemath.org/?q=onssar
> Graphs' layout may slightly vary from time to time, and so it may be worth
> it to click the [Evaluate] button a few times to get them placed nicely.
>
> Regards,
> Max
>
> On Sat, Sep 24, 2022 at 5:15 PM Max Alekseyev <maxale at gmail.com> wrote:
>
>> Hi Neil,
>>
>> I have written a piece of software that verified A352178(12) and
>> A352178(13) being equal to their lower bounds - 19 and 21, respectively.
>> I'll try to push this further.
>>
>> Regards,
>> Max
>>
>> On Thu, Sep 22, 2022 at 4:43 PM Neil Sloane <njasloane at gmail.com> wrote:
>>
>>> Dear Sequence Fans,
>>>
>>> Remember Stan Wagon's Powers of Two Problem? Brady Haran and I made a
>>> video
>>> a year ago that Brady released yesterday together with a postscript:
>>>
>>> Brady Haran and N. J. A. Sloane, <a
>>> href="https://youtu.be/IPoh5C9CcI8">Problems
>>> with Powers of Two</a>, Youtube Numberphile Video, Sep 21 2022
>>>
>>> Brady Haran and N. J. A. Sloane, <a href="
>>> https://www.numberphile.com/stop-press">STOP PRESS: Postscript to
>>> Problems
>>> with Powers of Two</a>, Sep 21 2022
>>>
>>> It has had 100K views already and there have been a lot of new results
>>> even
>>> today which you can see in https://oeis.org/A352178
>>>
>>> It's a lovely problem.
>>> Best regards
>>> Neil
>>>
>>> Neil J. A. Sloane, Chairman, OEIS Foundation.
>>> Also Visiting Scientist, Math. Dept., Rutgers University,
>>> Email: njasloane at gmail.com
>>>
>>> --
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>