Some Discrete Tomography Problems in Hypergraph Model Interpretation

In this paper we consider discrete tomography problems with an additional requirement of non-repeatability of rows of the binary matrix to be reconstructed; as well as discrete tomography problems with given pairwise projections. Representing the problems in the hypergraph model and pointing out their equivalence to the basic definitions, we state the following results: (i) nonconvexity of the set of hypergraphic sequences of simple hypergraphs with \(n\) vertices and \(m\) hyperedges in the \(n\) -dimensional \(m + 1\) -valued lattice, (ii) characterization of monotone Boolean functions associated with degree sequences of 3-/(n–3)-uniform hypergraphs, (iii) formulation of discrete tomography problems with paired projections, their connection to hypergraph degree sequence problem with generalized degrees, a solution for a particular case.