Equivalent classes of two-dimensional identical rectangle packing problem

Packing rectangular cartons into rectangular containers is an important task in manufacturing and distribution. The two-dimensional identical rectangles packing problem is to pack the maximum number of identical small rectangles of size a ≤ b (including a = b) into a large rectangle X ≤ Y. In this paper, the problem to discuss is, given the rectangle size (a, b), how many containers (large rectangles) are mutually nonequivalent under the equivalence definition provided?