[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 escribió:

> 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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>> 
> 
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