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matroid

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

Mathematics Subject Classification

05B35 no label found

Comments

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.

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