Square decomposition of a rectangle (Q1897480)

The author studies the minimum number of \(1\times 1\)-squares needed in a decomposition of an \(m\times n\)-rectangle in squares with integer side lengths from a given set \(A\cup \{1\}\), i.e. the uncovered area in an optimal packing of the rectangle by aligned squares with side lengths in \(A\). He determines these numbers exactly for decompositions in \(1\times 1\)-, \(2\times 2\)- and \(3\times 3\)-squares \((A= \{2, 3\})\) and gives bounds for other small \(A\).