The 1-Color Problem and the Brylawski Model

• S. Brocchi
• A. Frosini
• S. Rinaldi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)

Abstract

In discrete tomography, the 1-color problem consists in determining the existence of a binary matrix with row and column sums equal to some given input values arranged in two vectors. These two vectors are said to be compatible if the associated 1-color problem has at least a solution. Here, we start from a vector of projections, and we define an algorithm to compute all the vectors compatible with it, then we show how to arrange them in a partial order structure, and we point out some of its combinatorial properties. Finally, we prove that this poset is a sublattice of the Brylawski lattice too, and we check some common properties.

Keywords

Maximum Element Binary Matrix Combinatorial Property Integer Vector Vertical Projection
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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