set partition question

[miller.paul.w at gmail.com]

On May 25, 11:40 pm, pball.benet... at gmail.com wrote:

> This is a problem in statistical estimation. Given n records made up
> of k variables, define a cell as the point in the cartesian product of
> v_1 * v_2 * ... * v_k. I want to apply an estimator on the data in
> each cell.

So, basically, V = (v_1, v_2, ... , v_{k-1}, v_k) can be regarded as
an abstract, k-dimensional vector, right?

If I understand your revised problem statement correctly, what you
really want to do is build a graph of these vectors, where graph
adjacency is equivalent to adjacency in your sense.  That is, imagine
you have V_1, V_2, ... , V_n all sitting out in front of you,
represented abstractly as simple points.  Draw a line between V_i and
V_j if they are "adjacent" in your sense of the word.  What you have
then is a graph structure where your version of adjacency exactly
corresponds to graph adjacency.  Then, in your language, a stratum is
simply a path in this graph, and finding those is easy.

That is, unless I've got this all wrong. :-)