# [seqfan] Re: A possible new Keyword

Fri Sep 25 04:33:50 CEST 2015

```Not all of them. See A125106 and A242628.

-----Original Message-----
From: Max Alekseyev <maxale at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Thu, Sep 24, 2015 2:27 pm
Subject: [seqfan] Re: A possible new Keyword

I'd rather say that it is possible to enumerate partitions this way (not
that it
is based on an ordering of the partitions).
Also, this is very different from
other ordering of partitions, which
iterate over partitions of a fixed number
first.

Regards,
Max

On Thu, Sep 24, 2015 at 2:49 PM, Frank Adams-Watters
<franktaw at netscape.net>
wrote:

> Note that while you can do this without
thinking of partitions, it is in
> fact based on an ordering of the partitions:
A112798.
>
>
> -----Original Message-----
> From:
Max Alekseyev <maxale at gmail.com>
> To: Sequence Fanatics Discussion list
<seqfan at list.seqfan.eu>
> Sent: Thu, Sep 24, 2015 1:04 pm
> Subject: [seqfan]
Re: A possible new Keyword
>
>
> Notice that there is also a way to enter
coefficients of polynomials in
> infinite
> number of variables without
referring to partitions.
> This is what I call prime
> factorization order:
>
>
For n with the prime factorization n = p1^k1 * p2^k2 *
> ..., where p1=2,
>
p2=3, ... are the primes in their natural order (so only a
> finite number of
>
ki are nonzero),
> we let a(n) be the coefficient of u[1]^k1 *
> u[2]^k2 *
....
>
> E.g., multinomial coefficients C(k1+k2+...; k1, k2, ...)
> arranged
this way
> give http://oeis.org/A008480
>
> Regards,
> Max
>
>
>
> 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
> > Has this
problem appeared before?
> >
> > Best
> regards,
> > Juan Arias de Reyna
> >
>
>
> _______________________________________________
> >
> > Seqfan Mailing list
-
> http://list.seqfan.eu/
> >
>
>
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