... 1k, for 1 k d. For even d, Theorem 1.3 gives the CSP for faces of CP(d + 1, d), under the cyclic groupC = Zd+1action. In f act, it is straightforward to prove that this also holds for ... odd, d ≡ 3 (mo d 4)0 otherwise.which does not agree with h(n,d,d−1). For the C′′-case, one may come up with an artificial polynomial X(q) with the prop-erties X(1) = g(n, d, k) and X(−1) = ... we prove the CSP for faces of CP(n, d) for even d, along with a naturalq-analogue F (n, d, k; q) of the face number f (n, d, k), under an action of the cyclic groupC = Zn. For odd d, C is...