On Serial Symmetric Exchanges of Matroid Bases

Details On Serial Symmetric Exchanges of Matroid Bases On Serial Symmetric Exchanges of Matroid Bases

2011-10-09

arxiv.org/abs/1110.1826v3

Mathematics

Combinatorics

Scientific paper

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.

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