Abstract
A polyomino is a set of connected squares on a grid. In this paper we address the class of polyominoes with minimal perimeter for their area, and we show a bijection between minimal-perimeter polyominoes of certain areas.
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Work on this paper by both authors has been supported in part by ISF Grant 575/15.
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Notes
- 1.
In the sequel we simply say “monotone increasing.”.
References
Altshuler, Y., Yanovsky, V., Vainsencher, D., Wagner, I.A., Bruckstein, A.M.: On minimal perimeter polyminoes. In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds.) DGCI 2006. LNCS, vol. 4245, pp. 17–28. Springer, Heidelberg (2006). https://doi.org/10.1007/11907350_2
Asinowski, A., Barequet, G., Zheng, Y.: Enumerating polyominoes with fixed perimeter defect. In: Proceedings of 9th European Conference on Combinatorics, Graph Theory, and Applications, vol. 61, pp. 61–67. Elsevier, Vienna, August 2017
Barequet, G., Rote, G., Shalah, M.: \(\lambda > 4\): an improved lower bound on the growth constant of polyominoes. Commun. ACM 59(7), 88–95 (2016)
Bousquet-Mélou, M.: New enumerative results on two-dimensional directed animals. Discrete Math. 180(1–3), 73–106 (1998)
Bousquet-Mélou, M., Fédou, J.M.: The generating function of convex polyominoes: the resolution of a \(q\)-differential system. Discrete Math. 137(1–3), 53–75 (1995)
Broadbent, S., Hammersley, J.: Percolation processes: I. Crystals and mazes. In: Mathematical Proceedings of the Cambridge Philosophical Society, vol. 53, pp. 629–641. Cambridge University Press (1957)
Delest, M.P.: Generating functions for column-convex polyominoes. J. Comb. Theory Ser. A 48(1), 12–31 (1988)
Golomb, S.: Checker boards and polyominoes. Am. Math. Mon. 61(10), 675–682 (1954)
Jensen, I., Guttmann, A.: Statistics of lattice animals (polyominoes) and polygons. J. Phys. A: Math. Gen. 33(29), L257 (2000)
Klarner, D.: Cell growth problems. Can. J. Math. 19, 851–863 (1967)
Klarner, D., Rivest, R.: A procedure for improving the upper bound for the number of n-ominoes. Can. J. Math. 25(3), 585–602 (1973)
Ranjan, D., Zubair, M.: Vertex isoperimetric parameter of a computation graph. Int. J. Found. Comput. Sci. 23(04), 941–964 (2012)
Sieben, N.: Polyominoes with minimum site-perimeter and full set achievement games. Eur. J. Comb. 29(1), 108–117 (2008)
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Barequet, G., Ben-Shachar, G. (2018). Properties of Minimal-Perimeter Polyominoes. In: Wang, L., Zhu, D. (eds) Computing and Combinatorics. COCOON 2018. Lecture Notes in Computer Science(), vol 10976. Springer, Cham. https://doi.org/10.1007/978-3-319-94776-1_11
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DOI: https://doi.org/10.1007/978-3-319-94776-1_11
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