# Distinct Matroid Base Weights and Additive Theory

Chapter

## Summary

Let M be a matroid on a set E and let w : EG be a weight function, where G is a cyclic group. Assuming that w(E) satisfies the Pollard’s Condition (i.e., Every non-zero element of w(E) − w(E) generates G), we obtain a formula for the number of distinct base weights. If | G | is a prime, our result coincides with a result of Schrijver and Seymour. We also describe Equality cases in this formula. In the prime case, our result generalizes Vosper’s Theorem.

## Keywords

Additive inequalities Vosper’s theorem Weighted matroid

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