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Keywords:

  • matroid;
  • base;
  • serial symmetric exchange
  • 97N70;
  • 52B40;
  • 05B35

Abstract

We study some properties of a serial (i.e., one-by-one) symmetric exchange of elements of two disjoint bases of a matroid. We show that any two elements of one base have a serial symmetric exchange with some two elements of the other base. As a result, we obtain that any two disjoint bases in a matroid of rank 4 have a full serial symmetric exchange