Power Sum Polynomials in a Discrete Tomography Perspective

Power sum polynomials and the ghosts behind them

“…In [12] links were constructed between the problem of characterising subsets of PG(2, q) sharing the same power sum polynomial and the two-dimensional tomographic problem. The following definition was given.…”

“…In [12] the focus was mainly on the case q = p, and examples of simple ghosts were provided in such case, as lines and affine planes. However, there are wellknown structures which turn out to be ghosts and do not exist in the prime case.…”

“…In [12], the authors give some general results on the classification and the size of the point sets of PG(2, q) associated to a given power sum polynomial. More precisely, the right environment to study such a problem is the set of multi-subsets of PG(2, q), denoted by p PG (2,q) , where by multi-subset we mean a point subset of PG (2, q), with each point counted with a certain multiplicity modulo p (the field characteristic).…”

“…Reducing to simple sets, i.e., with no multiple points, ghosts are exactly the generalized Vandermonde sets defined in [14]. Moreover, in [12] the size of the subset of ghosts when q = p, namely, for prime fields, is determined.…”

“…The paper is organized as follows. In the next section we recall the basic definitions and the results obtained in [12], while in Sect. 3 we present new classes of simple ghosts.…”