S. Pagani, S. Pianta

Discrete tomography aims to recover the interior of an object, represented as a density function, from its projections along given directions. Discrete tomography is an interdisciplinary topic, with connections to several areas of Mathematics.
Usually, there is more than one function which agrees with a given set of projections. Ambiguities are due to functions having null projections along the considered directions, called ghosts. The algebraic description of all solutions of a tomographic problem, obtained by adding a suitable ghost to a solution, suggests a way of dealing with the subsets of the projective plane PG(2,q) related to a given polynomial.
In the finite geometry context, a homogeneous polynomial of degree q-1, called power sum polynomial, may be associated to a subset of PG(2,q). It is hard in general to classify all the subsets related to the same power sum polynomial.
After having established the connections between the two areas, we will introduce the geometric counterparts to the tomographic function sum and ghosts, and will show some recent results in the classification of the subsets of PG(2,q) sharing the same power sum polynomial.
Joint work with S. Pianta.

Keywords: Discrete tomography, ghost, multiset sum, power sum polynomial, projective plane


FB2 Heuristics 2
June 11, 2021  10:45 AM
2 - LV Kantorovich

Latest news

  • 6/5/21
    Conference abstract book

Cookie policy

We use cookies in order to be able to identify and authenticate you on the website. They are necessary for the correct functioning of it, and therefore they can not be disabled. If you continue browsing the website, you are agreeing with their acceptance, as well as our Privacy Policy.

Additionally, we use Google Analytics in order to analyze the website traffic. They also use cookies and you can accept or refuse them with the buttons below.

You can read more details about our Cookie Policy and our Privacy Policy.