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Hajdu Lajos (Debreceni Egyetem): An algebraic framework for discrete tomography and its applications

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Wednesday, 6. December 2017, 10:00 - 12:00
Abstract. The basic problem of discrete tomography is the following. Let S be a finite set of directions in Z^2. Can we reconstruct a finite set A of Z^2, knowing only the number of elements of A along the lines in the directions in S? (As maybe the simplest case: can we reconstruct a matrix having only elements 0 and 1, knowing only its row and column sums?) Then of course, several more questions arise, e.g. can we do that efficiently, what about uniqueness, etc. We note that the topic has several practical applications, e.g. in crystallography.
In the talk we outline an algebraic framework for discrete tomography (based upon generating functions, multivariate polynomials, the Chinese Remainder Theorem) developed together with R. Tijdeman. It turns out that this framework can be applied in several problems of discrete tomography. We shall present some of the applications, e.g. concerning the geometric placement of the solutions.
Location : Bolyai Intézet, I. emelet, Riesz terem, Aradi Vértanúk tere 1., Szeged


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