This paper studies the tomographical aspects of a new class of polyominoes, called permutominoes, which are defined by means of a pair of permutations. We inspect the classical problems of uniqueness and reconstruction on these objects, and in particular, using some combinatorial properties of their horizontal and vertical projections, we furnish a polynomial time reconstruction algorithm.
Reconstructing convex permutominoes / E. Barcucci; S. Brocchi; A. Frosini; S. Rinaldi. - In: PURE MATHEMATICS AND APPLICATIONS. - ISSN 1218-4586. - ELETTRONICO. - 20:(2009), pp. 113-125.
Reconstructing convex permutominoes
BARCUCCI, ELENA;BROCCHI, STEFANO;FROSINI, ANDREA;
2009
Abstract
This paper studies the tomographical aspects of a new class of polyominoes, called permutominoes, which are defined by means of a pair of permutations. We inspect the classical problems of uniqueness and reconstruction on these objects, and in particular, using some combinatorial properties of their horizontal and vertical projections, we furnish a polynomial time reconstruction algorithm.
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