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Wei-type duality theorems for matroids

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia

    Thomas Britz

  2. Department of Mathematics and Statistics, University of Tromsø, 9037, Tromsø, Norway

    Trygve Johnsen

  3. School of Mathematics, Statistics and Operations Research, Victoria University, P.O. Box 600, Wellington, 6140, New Zealand

    Dillon Mayhew

  4. Department of Mathematics and Engineering, Kumamoto University, 2-39-1, Kurokami, Kumamoto, 860-8555, Japan

    Keisuke Shiromoto

Authors
  1. Thomas Britz
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  2. Trygve Johnsen
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  3. Dillon Mayhew
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  4. Keisuke Shiromoto
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Corresponding author

Correspondence to Thomas Britz.

Additional information

Communicated by W. H. Haemers.

Thomas Britz was supported by an ARC Discovery Grant.

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Britz, T., Johnsen, T., Mayhew, D. et al. Wei-type duality theorems for matroids. Des. Codes Cryptogr. 62, 331–341 (2012). https://doi.org/10.1007/s10623-011-9524-y

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  • DOI: https://doi.org/10.1007/s10623-011-9524-y

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