Weight distribution of the bases of a binary matroid Original Research Article

Let M be a weighted binary matroid and w1 < … < wm be the increasing sequence of all possible distinct weights of bases of M. We give a sufficient condition for the property that w1, …, wm is an arithmetical progression of common difference d. We also give conditions which guarantee that wi+1 − wi ≤ d, 1 ≤ i ≤ m −1. Dual forms for these results are given also.