Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

If $E$ is a finite set and $k \in \mathbb{N}$, then the uniform matroid of rank $k$ is defined as the matroid generated by taking the collection of $k$ element subsets of $E$ as a basis. Is there an analog of this notion when $E$ is not finite?

Currently reading this paper, other references or examples would be great.

share|improve this question
    
Browsing the Wikipedia article suggests that there does not seem to be an agreed-upon definition of an infinite matroid. What definition are you using? –  Qiaochu Yuan Jun 15 '12 at 23:10
1  
@Qiaochu: The purpose of the cited paper is to give an axiomatic definition of infinitary matroids with duality; it actually gives five equivalent definitions, in terms of independent sets, bases, closure, circuits, and rank. It turns out that cardinality is too crude a measure, so a notion of relative rank is used that reduces to the usual notion in the finite case. –  Brian M. Scott Jun 15 '12 at 23:37
add comment

1 Answer

An uniform matroid is a matroid such that: $\forall I\in \mathcal{I}$, $\forall x\in I$, $\forall y\in E\backslash I$, $I-x+y\in \mathcal{I}$. Here some slides of a talk about the implications of the existance of infinite uniform matroids, http://settheory.mathtalks.org/wp-content/uploads/2014/03/Geschke.pdf

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.