Euclid meets Popeye: the Euclidean algorithm for \(2\times 2\) matrices (Q6117116)

In this paper the author studies a particular version of matrix reduction for size 2 square matrices with non-negative integer elements and positive determinant. The authors provide a formula on the number of reduced matrices whose determinant equals \(n\ge 1\). The result is proven using techniques of sails of lattices in the sense of Klein.