Polyominoes determined by permutations
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (2006).

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In this paper we consider the class of $\textit{permutominoes}$, i.e. a special class of polyominoes which are determined by a pair of permutations having the same size. We give a characterization of the permutations associated with convex permutominoes, and then we enumerate various classes of convex permutominoes, including parallelogram, directed-convex, and stack ones.
@article{DMTCS_2006_special_252_a2,
     author = {Fanti, I. and Frosini, A. and Grazzini, E. and Pinzani, R. and Rinaldi, S.},
     title = {Polyominoes determined by permutations},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities},
     year = {2006},
     doi = {10.46298/dmtcs.3478},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3478/}
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Fanti, I.; Frosini, A.; Grazzini, E.; Pinzani, R.; Rinaldi, S. Polyominoes determined by permutations. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (2006). doi : 10.46298/dmtcs.3478. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3478/

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