Suppose there are 2 base cells for a database of 100 dimensions, denoted as { (a1, a2, a3 , a100) :10, (a1, a2, b3 , b100) :10}, where each has a cell count of 10. If the minimum support is set to 10 then there will be (2^101)-6 distinct aggregate cells.

The reason being is there will be four duplicates. THE QUESTION IS: WHY ARE THESE THE ONLY four? Why wouldn't (a1, a2, a3, *....*) be a duplicate too?

(*,*,*...*)

(a1, a2, * ...*)

(a1, *,*...*)

(*, a2, *...*)

Why is there only four duplicates?