# matroid

## Primary tabs

Defines:
submodular inequality
Keywords:
combinatorics
Synonym:
independence structure
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:

## Mathematics Subject Classification

### Matroids, Definition 4, part b3)

Quote:

b3) If $S,T\in B$ and $x\in E-S$ then there exists $y\in E-T$
such that $(S\cup {x})-{y}\in B$.

-End quote.

Wouldn't the following:

b3) If $S,T\in B$ and $x\in T-S$ then there exists $y\in S-T$
such that $(S\cup {x})-{y}\in B$.

be logically equivalent, and a bit clearer?

In the other case covered by the existing b3), i.e. the case

$x\in E-T-S$

b3) becomes vacuously true, since you can just take y=x, so why not leave that case out.