Profile vectors in the lattice of subspaces (Q1043640)

Let \(\mathbb F_q\) be the finite field of \(q\) elements and let \(V\) be an \(n\)-dimensional vector space over \(\mathbb F_q\). For a family \(\mathcal U\) of subspaces of \(V\), the profile vector \(f(\mathcal U)\) is a vector \((x_0,\ldots,x_n)\) where \(x_i\) is the number of subspaces in \(\mathcal U\) of dimension \(i\) \((i=0,\ldots,n)\). In the paper under review the authors determine the profile polytope of interesting families (i.e., the convex hull of the profile vectors of all interesting families of subspaces).