[seqfan] Re: A possible new Keyword
Juan Arias de Reyna
arias at us.es
Thu Sep 24 18:00:12 CEST 2015
But my main problem is: how to include such a sequence of coefficients as
an entry in the OEIS? There are rules to include fractions, or to include
coefficients of a sequence of polynomials, or entries of a table.
But I do not know any rule in this case.
What I want is that given such a sequence I could find it in the OEIS
database. To accomplish this we need to write the coefficients in a standard order.
Best regards,
Juan
El 24/09/2015, a las 17:48, Neil Sloane escribiÃ³:
> rather than a new keyword, better to make an entry in the Index to the OEIS!
>
> 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 Thu, Sep 24, 2015 at 11:47 AM, Juan Arias de Reyna <arias at us.es> wrote:
>
>>
>> Frequently we consider sequences of polynomials in an infinite number of
>> variables.
>>
>> For example the fourth polynomial in a given sequence I find is
>>
>>> - u[1]^4 + 4 u[1]^2 u[2] - 2 u[2]^2 - 4 u[1] u[3] + 4 u[4]
>>
>> There is a coefficient for each partition of n = 4. In this case each
>> coefficient is
>> related to a partition of 4
>>
>> 4 = 1 + 1 + 1 + 1 coef -1
>> = 1 + 1 + 2 coef 4
>> = 1 + 3 coef -4
>> = 2 + 2 coef -2
>> = 4 coef 4
>>
>>
>> To include the sequence of coefficients we want to give a canonical order
>> to
>> all possible partitions.
>> I will consider useful that all partition of the number n precede all
>> partitions of n+1.
>>
>> But how to order the partitions of a number n?
>> Perhaps writing the summands in increasing order and then by lexicografic
>> order as I have
>> written above the partitions of 4.
>>
>> Maybe somebody here in OEIS has a better election.
>> I will like to fix a particular order,
>> then in all cases that a sequence of
>> this type is included in OEIS this same order should be used. Also a new
>> keyword as the
>> actual tabf and tabl should be added to the Keywords file, to indicate
>> this type of sequence.
>>
>>
>> Somebody know sequences of this type already included in OEIS?
>> Has this problem appeared before?
>>
>> Best regards,
>> Juan Arias de Reyna
>>
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>>
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