Asymptotic analysis and random sampling of digitally convex polyominoes

Authors:
O. Bodini;Ph. Duchon;A. Jacquot;L. Mutafchiev
Affiliations:
LIPN, Université Paris 13, Villetaneuse, France;LaBRI, Talence cedex, France;LIPN, Université Paris 13, Villetaneuse, France;American University in Bulgaria, Blagoevgrad, Bulgaria,Institute of Mathematics and Informatics, Sofia, Bulgaria
Venue:
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Year:
2013

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Abstract

Recent work of Brlek et al. gives a characterization of digitally convex polyominoes using combinatorics on words. From this work, we derive a combinatorial symbolic description of digitally convex polyominoes and use it to analyze their limit properties and build a uniform sampler. Experimentally, our sampler shows a limit shape for large digitally convex polyominoes.