Typo in A0077221 ? [more graphical partitions]

[Dean Hickerson]

Gordon Royle wrote:

> PS The term 'graphical partition' is inconsistently used throughout  
> these entries - as Frank Ruskey said, it really should be restricted  
> to partitions of a fixed integer (thus fixing the number of edges of  
> the graphs) but it is used in both this sense, and the above sense  
> (fixing number of vertices) often with very limited explanation... it  
> might be quite a major undertaking to fix them all up though.

I don't see what the problem is.  A 'partition' is simply a finite multiset
of positive integers, and that's how the term is being used here.  Partitions
have several numerical attributes that are important in different contexts,
such as the sum of the parts, the number of parts, the rank, etc.  Usually
when we're counting partitions, we're most interested in the sum of the
parts, but in this context the number of parts is more relevant, since
it equals the number of vertices of the graph.

Dean Hickerson
dean at math.ucdavis.edu