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Fixing Numbers for Matroids

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Abstract

Motivated by work in graph theory, we define the fixing number for a matroid. We give upper and lower bounds for fixing numbers for a general matroid in terms of the size and maximum orbit size (under the action of the matroid automorphism group). We prove the fixing numbers for the cycle matroid and bicircular matroid associated with 3-connected graphs are identical. Many of these results have interpretations through permutation groups, and we make this connection explicit.

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Authors and Affiliations

  1. Department of Mathematics, Lafayette College, Easton, PA, 18042, USA

    Gary Gordon

  2. Department of Mathematical Sciences, University of Montana, Missoula, MT, 59812, USA

    Jennifer McNulty

  3. Department of Mathematics and Computer Science, Pacific University, Forest Grove, OR, 97116, USA

    Nancy Ann Neudauer

Authors
  1. Gary Gordon
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  2. Jennifer McNulty
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  3. Nancy Ann Neudauer
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Correspondence to Gary Gordon.

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Gordon, G., McNulty, J. & Neudauer, N.A. Fixing Numbers for Matroids. Graphs and Combinatorics 32, 133–146 (2016). https://doi.org/10.1007/s00373-015-1540-7

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  • DOI: https://doi.org/10.1007/s00373-015-1540-7

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