About: Partition matroid

In mathematics, a partition matroid or partitional matroid is a matroid that is a direct sum of uniform matroids. It is defined over a base set in which the elements are partitioned into different categories. For each category, there is a capacity constraint - a maximum number of allowed elements from this category. The independent sets of a partition matroid are exactly the sets in which, for each category, the number of elements from this category is at most the category capacity.