Hi,
On 2013-04-15, Simon King <simon.k...@uni-jena.de> wrote:
> I have a finite set X and a set S of subsets of X. I'd like to get a
> list (or better: an iterator) of all subsets U of S (i.e., subsets of
> subsets) such that the union of the elements of U is equal to X.
> Ideally, I'd like that the number of intersection points (counted with
> multiplicity) of elements of U is ascending.
>
> Hence, if there is a disjoint cover of X by elements of S, then I'd like
> to get this first, and otherwise I'd like to first get a cover that is "as
> close to being disjoint as possible".
I have found that one can get disjoint ("exact") covers via "dancing
links".
But let me formulate a related problem that I'd even more like to solve:
Given a matrix M over some finite field F, I need a linear combination
of rows of M such that the resulting row has all coefficients non-zero
(in F). Preferably, the set of rows to be combined should be small, but
it is not needed that it is minimal.
How can this be done?
Best regards,
Simon
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