Flag (linear Algebra) - Set-theoretic Analogs

Set-theoretic Analogs

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 groups and algebraic groups.

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) corresponds to the ordering .