The direct sum of q-matroids

For classical matroids, the direct sum is one of the most straightforward methods to make a new matroid out of existing ones. This paper defines a direct sum for q -matroids, the q -analogue of matroids. This is a lot less straightforward than in the classical case, as we will try to convince the reader. With the use of submodular functions and the q -analogue of matroid union we come to a definition of the direct sum of q -matroids. As a motivation for this definition, we show it has some desirable properties.