[Solved]: Name for concept: each pair of sets is either nested or disjoint

Problem Detail: 

Does this property have a name?

Given a collection of sets $\mathcal{P}$, for all pairs $A, B\in\mathcal{P}$, either $A\cap B=\emptyset$ or $A\subseteq B$ or $B\subseteq A$.

This concept could equally apply to monoids, groups, partial orders or other mathematical structures, with some adjustments to the definitions. For instance, for monoids and groups we would replace $A\cap B=\emptyset$ by $A\cap B=\{\epsilon\}$, where $\epsilon$ is the unit of the monoid/group.

Asked By : Dave Clarke

Answered By : adrianN

I think that's called a laminar family.

Best Answer from StackOverflow

Question Source : http://cs.stackexchange.com/questions/14280

3.2K people like this

 Download Related Notes/Documents