Weight distribution of the bases of a binary matroid

Abstract

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. © 1998 Elsevier Science Ltd. All rights reserved.