Designs, Codes and Cryptography

, Volume 62, Issue 3, pp 331–341 | Cite as

Wei-type duality theorems for matroids

  • Thomas Britz
  • Trygve Johnsen
  • Dillon Mayhew
  • Keisuke Shiromoto


We present several fundamental duality theorems for matroids and more general combinatorial structures. As a special case, these results show that the maximal cardinalities of fixed-ranked sets of a matroid determine the corresponding maximal cardinalities of the dual matroid. Our main results are applied to perfect matroid designs, graphs, transversals, and linear codes over division rings, in each case yielding a duality theorem for the respective class of objects.


Matroid duality theorems Demi-matroid Poset code Wei’s Duality Theorem Matroid design 

Mathematics Subject Classification (2000)

05B35 06A07 94B05 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Thomas Britz
    • 1
  • Trygve Johnsen
    • 2
  • Dillon Mayhew
    • 3
  • Keisuke Shiromoto
    • 4
  1. 1.School of Mathematics and StatisticsUniversity of New South WalesSydneyAustralia
  2. 2.Department of Mathematics and StatisticsUniversity of TromsøTromsøNorway
  3. 3.School of MathematicsStatistics and Operations Research, Victoria UniversityWellingtonNew Zealand
  4. 4.Department of Mathematics and EngineeringKumamoto UniversityKumamotoJapan

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