Power sum polynomials in a discrete tomography perspective

Risultato della ricerca: Contributo in libroContributo a convegno

Abstract

For a point of the projective space $PG(n,q)$, its R'edei factor is the linear polynomial in $n+1$ variables, whose coefficients are the point coordinates. The power sum polynomial of a subset $S$ of $PG(n,q)$ is the sum of the $(q-1)$-th powers of the R'edei factors of the points of $S$. The fact that many subsets may share the same power sum polynomial offers a natural connection to discrete tomography. In this paper we deal with the two-dimensional case and show that the notion of ghost, whose employment enables to find all solutions of the tomographic problem, can be rephrased in the finite geometry context, where subsets with null power sum polynomial are called ghosts as well. In the latter case, one can add ghosts still preserving the power sum polynomial by means of the multiset sum (modulo the field characteristic). We prove some general results on ghosts in $PG(2,q)$ and compute their number in case $q$ is a prime.
Lingua originaleEnglish
Titolo della pubblicazione ospiteDiscrete Geometry and Mathematical Morphology
Pagine325-337
Numero di pagine13
Volume12708
DOI
Stato di pubblicazionePubblicato - 2021
EventoDGMM 2021 - Uppsala, Svezia (online)
Durata: 24 mag 202127 mag 2021

Convegno

ConvegnoDGMM 2021
CittàUppsala, Svezia (online)
Periodo24/5/2127/5/21

Keywords

  • Discrete tomography
  • Ghost
  • Multiset sum
  • Power sum polynomial
  • Projective plane

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