Complete partitions

[Augustine Munagi]

Oh! I see your point.
But your condition is not sufficient. 2+3+3  fulfills your condition,
but not complete since it does not contain the partition of 1. Also
2+2+4, etc.


On 3/23/07, franktaw at netscape.net <franktaw at netscape.net> wrote:
> This is (essentially) the definition used by this sequence.  Viz, the
> existing comment in the sequence: " A partition of n is complete if
> every number 1 to n can be represented as a sum of parts of the
> partition."  My comment is to show an alternative condition for
> completeness (in this sense), not an alternative definition.
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: aomunagi at gmail.com
>
>  Hi,
>  This seems like the newest meaning to be associated with "complete".
>
>  For instance
>
>  ...
>
>  Complete partition (Fibonacci Quart. 36 (1998) 354–360) => a partition
>  of n is complete if each smaller integer can be written as a linear
>  combination of its parts with coefficients in {0,1}.
>
>  ...
>
>  Augustine
>
>  On 3/23/07, franktaw at netscape.net <franktaw at netscape.net> wrote:
>  > I just sent in the following comment:
>  >
>  ...
>  > %N A126796 Number of complete partitions of n.
>  > %C A126796 A partition is complete iff each part is no more than 1
> more
>  > than the sum of all smaller parts.
>
> ________________________________________________________________________
> Check Out the new free AIM(R) Mail -- 2 GB of storage and
> industry-leading spam and email virus protection.
> =0
>


-- 
Augustine O. Munagi
The John Knopfmacher Centre for Applicable Analysis and Number Theory
School of Mathematics
University of the Witwatersrand
Johannesburg 2050
South Africa
Phone: 27-11-717-6246
Fax: 27-11-717-6259