Striking out rows and columns intersecting on a diagonal will always leave some surviving elementary determinants, until so many have been stricken out that it is no longer possible to form a complete determinant. The coefficient of the elementary determinants will depend on how much of the remaining elementary determinant can be salvaged.
In general, the determinant of the de Bruijn 
factorizes,
so that
where the factors are 
determinants obtained by varying the
indices i and j with fixed 
To get the minor of the hz,hz
diagonal element, we need to consider two cases. If this pivot does not
belong to any subdeterminant, it can be ignored. If it does, we drop the
z,z term from the product, replacing it by the internal minor from
within the omitted factor. Thus
