A tiling system for the class of L-convex polyominoes

Authors:
S. Brocchi;A. Frosini;R. Pinzani;S. Rinaldi
Affiliations:
Università di Firenze, Dipartimento di Sistemi e Informatica, viale Morgagni 65, 50134 Firenze, Italy;Università di Firenze, Dipartimento di Sistemi e Informatica, viale Morgagni 65, 50134 Firenze, Italy;Università di Firenze, Dipartimento di Sistemi e Informatica, viale Morgagni 65, 50134 Firenze, Italy;Università di Siena, Dipartimento di Scienze Matematiche e Informatiche, Pian dei Mantellini 44, 53100 Siena, Italy
Venue:
Theoretical Computer Science
Year:
2013

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Abstract

A polyomino is said to be L-convex if any two of its cells can be connected by a path entirely contained in the polyomino, and having at most one change of direction. In this paper, answering a problem posed by Castiglione and Vaglica [6], we prove that the class of L-convex polyominoes is tiling recognizable. To reach this goal, first we express the L-convexity constraint in terms of a set of independent properties, then we show that each class of convex polyominoes having one of these properties is tiling recognizable.