# Definition:Fundamental Circuit (Matroid)

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## Definition

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

Let $B$ be a base of $M$.

Let $x \in S \setminus B$.

The fundamental circuit of $x$ in the base B, denoted $\map C {x, B}$, is the unique circuit such that:

$x \in \map C {x, B} \subseteq B \cup \set x$