---
tag: J517QKT7CQ
kind: concept
name: Base-orderable matroid
sources:
  - wikipedia: en:65674252@r1154271040
    locator: Base-orderable matroid
    note: adopted
    mention: wikipedia://en/65674252
    sections: [Summary]
same_as:
  wikidata: Q104866040
  wikipedia: Base-orderable matroid
inventory: [CEVWVZPDEV]
---

## Summary

In mathematics, a **base-orderable matroid** is a matroid that has the following additional property, related to the bases of the matroid.

> 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.

The property was introduced by Brualdi and Scrimger. A **strongly-base-orderable matroid** has the following stronger property:

> 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.