Editing Flag (linear algebra) (section)

==Set-theoretic analogs==
{{Further|Field with one element}}
From the point of view of the [[field with one element]], a set can be seen as a vector space over the field with one element: this formalizes various analogies between [[Coxeter group]]s and [[algebraic group]]s.

Under this correspondence, an ordering on a set corresponds to a maximal flag: an ordering is equivalent to a maximal filtration of a set. For instance, the filtration (flag) <math>\{0\} \subset \{0,1\} \subset \{0,1,2\}</math> corresponds to the ordering <math>(0,1,2)</math>.