Definition:Isomorphism (Matroid)
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Definition
Let $M_1 = \struct{S_1, \mathscr I_1}$ and $M_2 = \struct{S_2, \mathscr I_2}$ be matroids.
Let $f : S_1 \to S_2$ be a bijection.
Then $f$ is called an isomorphism if and only if:
- $\forall X \subseteq S : X \in \mathscr I_1 \iff \map f X \in \mathscr I_2$
If $f$ is an isomorphism then $M_1$ is said to be isomorphic to $M_2$.
Sources
- 1976: Dominic Welsh: Matroid Theory ... (previous) ... (next) Chapter $1.$ $\S 2.$ Axiom Systems for a Matroid