Complete partitions

franktaw at franktaw at
Fri Mar 23 08:09:28 CET 2007

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

 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}.



 On 3/23/07, franktaw at <franktaw at> 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 
 > than the sum of all smaller parts.

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