Our paper on the Interaction between skew-representability, tensor products, extension properties, and rank inequalities was accepted to SODA! The paper explores skew-representable matroids, a fundamental class connecting combinatorics and linear algebra with applications in coding theory, optimization, and geometry. Since deciding skew-representability is computationally hard, we study it through a new perspective: tensor products. This approach gives a characterization of skew-representable matroids, shows that non-representability can be certified, and yields new structural insights such as tensoring rank-3 matroids with uniform ones. As an application, we reprove Ingleton’s inequality and establish the first linear rank inequality for folded skew-representable matroids that does not follow from the common information property. Turns out even skew-representability enjoys a good SODA 🙂