[seqfan] Re: A possible new Keyword

Frank Adams-Watters franktaw at netscape.net
Thu Sep 24 18:39:46 CEST 2015


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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