A flag $f$-vector is a sort of refining of the $f$-vector of a convex polytope $P$ which gives you more information about the facial structure of $P$. We go over the definition of a flag $f$-vector and show how to compute the flag $f$-vector for the Coxeter complex using descents. We then review the topics of even signed permutations and covectors in projective space. If we have time we'll show a bijection between even signed permutations with a single descent and covectors in projective space and extend this bijection to certain parabolic cosets in the type $B_n$ Coxeter group with certain chains of covectors.