A new class of matroids (Q2474652)

The author continues the study of classes of \(k\)-balanced matroids, by exploring the operations that preserve the \(k\)-balanced property of a matroid. So he establishes that the amalgam of two uniform matroids is \(k\)-balanced if and only if the \(k\)-densities of the two matroids are at most the \(k\)-density of their amalgam. Conditions for the parallel connection and subsequently the connection of uniform matroids to be \(k\)-balanced are also established.