[seqfan] Re: Generalization of A005646

[William Keith]

On Jan 1, 2010, at 6:24 PM, Robert Munafo wrote:

> You say "more than 2-way partitions are allowed".
>
> Is it also required that each partition is 3-way, or can it be a mix  
> of
> partitions of 2-way and/or 3-way?
>
> (If the former, I suppose the value would be 0 for N=1, *undefined*  
> for N=2,
> and 1 for N-3)

I believe his meaning is that answers can be more than "yes and no";  
the classification is permitted to ask, e.g., "animal, vegetable or  
mineral"?  So there are two classifications of three objects: one that  
divides the objects 1-and-2 followed by a second question that  
distinguishes the latter 2, and one classification that distinguishes  
all three immediately.

William Keith