The sum of matroids II

Abstract

For all the applications in Chapter 12 we needed quick algorithm for the matroid partition problem: Given the matroids M ₁ = (S, F ₁), M ₂ = (S, F ₂), ..., M _k = =(S, F _k ) with respective rank functions r ₁, r ₂, ..., r _k , and given a subset X ⊆ S. One should decide whether X is independent in the sum \({\text{N = V}}_{i = 1}^k {\text{M}}_i\) of the matroids.