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