Definition:Parallel (Matroid)

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Definition

Let $M = \struct{S, \mathscr I}$ be a matroid.


Two elements $x, y \in S$ are said to be parallel in $M$ If they are not loops but $\set{x,y}$ is a dependent subset of $S$.


That is, $x, y \in S$ are parallel if:

$\set x, \set y \in \mathscr I$ and $\set{x, y} \not \in \mathscr I$.

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