THE NUMBER OF SUBSPACES OF A VECTOR SPACE.

Abstract : The number G sub n of subspaces of an n-dimensional vector space over GF(q) is studied by the symbolic calculus. This calculus provides a general technique for proving theorems in particular identities, involving the G sub n and the Gaussian coefficient (n, k). Examples include a recursion for the G sub n, an infinite product expansion for the Eulerian generating function of the G sub n, and a q-analog of the Pascal triangle for the (n, k). (Author)