[seqfan] Re: Polyominoes (A000105, A000988, A001168) - offset problem

Fred Lunnon fred.lunnon at gmail.com
Thu Jun 25 21:12:53 CEST 2020


  Or indeed,
    https://en.wikipedia.org/wiki/Field_with_one_element

  Such questions may prove highly nontrivial, and their detailed investigation
reveal subtle disparities between apparently equivalent concepts, as well as
unexpected connections between apparently distinct ones.

  Didactically convenient simplified responses should therefore be avoided
--- but just don't mention  b*n*m*a* c*e*f*c*e*t*  !

WFL


On 6/25/20, Christian Lawson-Perfect <christianperfect at gmail.com> wrote:
> This feels like the discussion about whether empty matrices exist. See "An
> empty exercise" by Carl de Boor -
> https://dl.acm.org/doi/10.1145/122272.122273
>
> On Thu, 25 Jun 2020 at 13:15, Jean-Luc Manguin <jean-luc.manguin at unicaen.fr>
> wrote:
>
>> Hello everyone,
>>
>> Thank you Brendan to "bring some water to my mill", and I am sorry to
>> "shake the tree up to the top", but a request (actually 3) on OEIS with
>> "number of fixed/one-sided/free polyominoes" give results that show this
>> question is not definitely clear.
>> Moreover, the sequences such as A292357 could be strangely impacted if we
>> admit that there is a "zeromino" ; in that case, we should complete the
>> first diagonal with a "1" at the beginning (if I follow your hypothesis),
>> but what should we put in the corresponding line and row ?? And what could
>> mean "a polyomino with height = 0 and width = n" ??
>> And moreover again, why should we consider there is ONE zeromino ? Why not
>> zero ?
>>
>> The usual "rule" is (IMO) to exhibit a publication which justify such a
>> choice ; till now, I have seen nothing.
>>
>> Thank you for your attention.
>> Best regards,
>>
>> JLM
>>
>> ----- Mail original -----
>> De: "Brendan McKay" <Brendan.McKay at anu.edu.au>
>> À: "seqfan" <seqfan at list.seqfan.eu>
>> Envoyé: Jeudi 25 Juin 2020 11:15:55
>> Objet: [seqfan] Re: Polyominoes (A000105, A000988, A001168) - offset
>> problem
>>
>> Hi Neil,
>>
>> Anyone who sees an error on Wikipedia, and knows how to fix it but
>> doesn't, is
>> responsible for the error.
>>
>> But in this case there is no error.  Wikipedia follows "reliable
>> sources" and in this case
>> the reliable source is Golumb's book "Polyominoes".  From a brief look
>> it seems that
>> Golumb does not recognise a null polyomino (see Fig 1 and Tables 3 and
>> D.1), so
>> Wikipedia is *required* to either also disallow it or to change to a
>> different source.
>>
>> Incidentally, the first comment on A0000105, which is
>> "A0000105(n) + A030228(n) = A000988(n)", is not correct for n=0 at the
>> moment.
>>
>> Cheers, Brendan.
>>
>> On 25/6/20 5:27 pm, Neil Sloane wrote:
>> > Everything in the Wikipedia is inaccurate.
>>
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>>
>>
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