The number of convex polyominoes reconstructible from their orthogonal projections

DOI10.1016/S0012-365X(96)83007-XzbMath0856.05024OpenAlexW2051713785MaRDI QIDQ1924359

Maurice Nivat, Renzo Pinzani, Alberto del Lungo

Publication date: 24 February 1997

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0012-365x(96)83007-x

zbMATH Keywords

reconstructionorthogonal projectionsconvex polyominoes

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Polyominoes (05B50)

Related Items (18)

Reconstruction of convex polyominoes with a blocking component ⋮ Polyominoes defined by their vertical and horizontal projections ⋮ Tomographic reconstruction of 2-convex polyominoes using dual Horn clauses ⋮ Properties of SAT formulas characterizing convex sets with given projections ⋮ Recognizable Picture Languages and Polyominoes ⋮ Discrete tomography for inscribable lattice sets ⋮ A reconstruction algorithm for L-convex polyominoes. ⋮ Reconstruction of domino tiling from its two orthogonal projections ⋮ Reconstruction of 8-connected but not 4-connected \(hv\)-convex discrete sets ⋮ X-rays characterizing some classes of discrete sets ⋮ Reconstruction of 4- and 8-connected convex discrete sets from row and column projections ⋮ Further steps on the reconstruction of convex polyominoes from orthogonal projections ⋮ Reconstruction of convex polyominoes from orthogonal projections of their contours ⋮ An experimental study of the stability problem in discrete tomography ⋮ Reconstruction of Discrete Sets from Four Projections: Strong Decomposability ⋮ Detection of the discrete convexity of polyominoes ⋮ Reconstruction of convex 2D discrete sets in polynomial time ⋮ Basic analytic combinatorics of directed lattice paths

Cites Work

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• Three-dimensional object reconstruction from orthogonal projections
• Switching components and the ambiguity problem in the reconstruction of pictures from their projections
• Polyominoes defined by two vectors
• Characterization of Binary Patterns and Their Projections
• The reconstruction of binary patterns from their projections
• Reconstruction of pictures from their projections

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