Distinct Matroid Base Weights and Additive Theory
Combinatorics
2009-03-05 v1 Number Theory
Abstract
Let be a matroid on a set and let be a weight function, where is a cyclic group. Assuming that satisfies the Pollard's Condition (i.e. Every non-zero element of generates ), we obtain a formulae for the number of distinct base weights. If is a prime, our result coincides with a result Schrijver and Seymour. We also describe Equality cases in this formulae. In the prime case, our result generalizes Vosper's Theorem.
Cite
@article{arxiv.0903.0642,
title = {Distinct Matroid Base Weights and Additive Theory},
author = {Y. O. Hamidoune and I. P. da Silva},
journal= {arXiv preprint arXiv:0903.0642},
year = {2009}
}