Definitions: Flock, Non-flat Cone, Coordinate Function

Proposition 8.1: If F is a flock of a non-flat cone, then the coordinate functions of F are permutations of GF(q).

Pf: Since the cone C(V, S) is non-flat, we may, by recoordinatizing , assume that the points A = (1,0,0,0), B = (0,1,0,0) and C = (0,0,1,0) are in S. The induced permutations on the generators at these points are f(t), g(t) and h(t) respectively.

Return to Herd Spaces and Herds