The Number of Line-Convex Directed Polyominoes Having the Same Orthogonal Projections
The number of line-convex directed polyominoes with given horizontal and vertical projections is studied. It is proven that diagonally convex directed polyominoes are uniquely determined by their orthogonal projections. The proof of this result is algorithmical. As a counterpart, we show that ambiguity can be exponential if antidiagonal convexity is assumed about the polyomino. Then, the results are generalised to polyominoes having convexity property along arbitrary lines.
KeywordsDiscrete tomography line-convex directed polyomino reconstruction from projections
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