I just fixed the somewhat confusing wording in the introduction which talked about a constant intersection.
I believe the right concept is that the intersection is common.
If a set of sets have pairwise intersections that are different, those are still constants, if the sets being considered are constants! E.g. { 1, 2, 3, 4, 5 } is a constant set, so is the { 2 } which is an intersection of { 1, 2 } and { 2, 3 }, and so is { 4 }, which is an intersection of { 3, 4 } and { 1, 4 }.
(I get that the idea is that the intersection constant from pair to pair: i.e. if we enumerate the pairs as an index i from 0 to n-1, then the intersection doesn't vary with i.)
Under the formal definition, I replaced the explanatory ("in other words") text with a different idea, instead of reiterating what's already in the introduction.
Every element in U is either common to all the subsets in W, or else is found in at most one W subset. No elements are shared by some sets in W, but not others.
I believe the right concept is that the intersection is common.
If a set of sets have pairwise intersections that are different, those are still constants, if the sets being considered are constants! E.g. { 1, 2, 3, 4, 5 } is a constant set, so is the { 2 } which is an intersection of { 1, 2 } and { 2, 3 }, and so is { 4 }, which is an intersection of { 3, 4 } and { 1, 4 }.
(I get that the idea is that the intersection constant from pair to pair: i.e. if we enumerate the pairs as an index i from 0 to n-1, then the intersection doesn't vary with i.)
Under the formal definition, I replaced the explanatory ("in other words") text with a different idea, instead of reiterating what's already in the introduction.
Every element in U is either common to all the subsets in W, or else is found in at most one W subset. No elements are shared by some sets in W, but not others.