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  "body": "\n## Summary\n\nIn mathematics, a **base-orderable matroid** is a matroid that has the following additional property, related to the bases of the matroid.\n\n\u003e For any two bases $A$ and $B$ there exists a **feasible exchange [[bijection|0GG9TVW90M]]**, defined as a bijection *$f$* from *$A$* to $B$, such that for every $a\\in A\\setminus B$, both $(A \\setminus \\{ a \\}) \\cup \\{f(a)\\}$ and $(B \\setminus \\{ f(a) \\}) \\cup \\{a\\}$ are bases.\n\nThe property was introduced by Brualdi and Scrimger. A **strongly-base-orderable matroid** has the following stronger property:\n\n\u003e For any two bases $A$ and $B$, there is a **strong feasible exchange bijection**, defined as a bijection *$f$* from *$A$* to $B$, such that for every $X\\subseteq A$, both $(A \\setminus X) \\cup f(X)$ and $(B \\setminus f(X)) \\cup X$ are bases.\n",
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