[seqfan] Re: A possible new Keyword

Juan Arias de Reyna arias at us.es
Thu Sep 24 18:55:22 CEST 2015


Thanks, 

This appear to solve my main question. 
Not in the best ideal way, because of the two orderings. 


Best regards, 
Juan



El 24/09/2015, a las 18:39, Frank Adams-Watters escribió:

> There are two standard orderings of the partitions in the OEIS. One is the "Abramowitz and Stegun" ordering in A036036 (and A036037 is the same ordering). The other is the "Mathematica" ordering in A080577. Ideally, you should enter your sequence twice, once with each of these. If that's two much work, just use one or the other. Be sure to document what ordering is used in each case.
> 
> Franklin T. Adams-Watters
> 
> -----Original Message-----
> From: Juan Arias de Reyna <arias at us.es>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Thu, Sep 24, 2015 10:47 am
> Subject: [seqfan] A possible new Keyword
> 
> 
> 
> 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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