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Distinct Matroid Base Weights and Additive Theory

  • Y. O. HamidouneEmail author
  • I. P. da Silva
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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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Université Pierre et Marie Curie, E. CombinatoireParisFrance
  2. 2.CELC/Universidade de Lisboa, Faculdade de CiênciasCampo GrandeLisboaPortugal

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