Multiset Signatures and Partitions

[Jon Wild]

On Tue, 17 Jan 2006, franktaw at netscape.net wrote:

> Let us define the signature of a (finite) multiset to be the partition 
> composed of the multiplicities of the members of the multiset.  For 
> example, for the multiset {1,1,1,1,2,2,3,4}, the signature is {1,1,2,4}. 
> The prime signature of a number is then the signature of its prime 
> factor multiset.

> Since a partition is also a multiset,

Frank and others - you might be interested in A096443, the number of 
partitions of the nth multiset. Multisets (represented as partitions) are 
ordered the same way Richard Guy suggested the other day, and the sequence 
gives the number of partitions of the multiset.

Best regards -Jon Wild