# [seqfan] Re: A possible new Keyword

Neil Sloane njasloane at gmail.com
Thu Sep 24 17:48:32 CEST 2015

```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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