Power Sum Polynomials in a Discrete Tomography Perspective

For a point of the projective space \(\text {PG}(n,q)\), its Redei factor is linear polynomial in \(n+1\) variables, whose coefficients are coordinates. The power sum subset S {PG}(n,q)\) \((q-1)\)-th powers factors points S. fact that many subsets may share same offers natural connection to discrete tomography. In this paper we deal with two-dimensional case and show notion ghost, employment enables find all solutions tomographic problem, can be rephrased finite geometry context, where null called ghosts as well. latter case, one add still preserving by means multiset (modulo field characteristic). We prove some general results on {PG}(2,q)\) compute their number q prime.