The number of line-convex directed polyominoes having the same orthogonal projections

Authors:
Péter Balázs
Affiliations:
Department of Computer Algorithms and Artificial Intelligence, University of Szeged, Szeged, Hungary
Venue:
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Year:
2006

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Abstract

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.