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Two subclasses of 2-convex polyominoes: properties for reconstruction
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A polyomino P is called 2-convex if for every two cells there exists a monotone path included in P with at most 2 changes of direction. This paper studies the tomographical aspects of two subclasses of 2-convex polyominoes called ?2L and ??2L. In the first part, the uniqueness results of the two subclasses of HV - convex polyominoes ? and ?? are investigated using the switching components (that is the elements of these subclasses that have the same projections). In the second part, using the uniqueness results and the algorithm by Chrobak and D?rr, two paths connecting the feet and a tomographical condition are given to verify whether P is in ?2L or ??2L.
Title: Two subclasses of 2-convex polyominoes: properties for reconstruction
Description:
A polyomino P is called 2-convex if for every two cells there exists a monotone path included in P with at most 2 changes of direction.
This paper studies the tomographical aspects of two subclasses of 2-convex polyominoes called ?2L and ??2L.
In the first part, the uniqueness results of the two subclasses of HV - convex polyominoes ? and ?? are investigated using the switching components (that is the elements of these subclasses that have the same projections).
In the second part, using the uniqueness results and the algorithm by Chrobak and D?rr, two paths connecting the feet and a tomographical condition are given to verify whether P is in ?2L or ??2L.
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