Power sum polynomials and the ghosts behind them
Journal article, 2023

The power sum polynomial associated to a multi-subset of the projective plane PG (2 , q) is the sum of the (q- 1) -th powers of the Rédei factors of the points in the multi-subset. The classification of multi-subsets having the same power sum polynomial passes through the determination of those multi-subsets associated to the zero polynomial, called ghosts. In this paper we provide new classes of ghosts and compute the dimension of the ghost subspace by exploiting the linear code generated by the lines of PG (2 , q) and its dual. Moreover, we explicitly enumerate and classify ghosts for planes of order 2, 3, 4.


multiset sum

projective plane

power sum polynomial


Marco L. Della Vedova

Chalmers, Mechanics and Maritime Sciences (M2), Vehicle Engineering and Autonomous Systems

Silvia M.C. Pagani

Università Cattolica del Sacro Cuore

Silvia Pianta

Università Cattolica del Sacro Cuore

Journal of Geometry

0047-2468 (ISSN) 1420-8997 (eISSN)

Vol. 114 1 1

Subject Categories

Algebra and Logic


Mathematical Analysis



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