Properties of Minimal-Perimeter Polyominoes

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.

[1]  Andrei Asinowski,et al.  Enumerating Polyominoes with Fixed Perimeter Defect , 2017, Electron. Notes Discret. Math..

[2]  J. Hammersley,et al.  Percolation processes , 1957, Mathematical Proceedings of the Cambridge Philosophical Society.

[3]  Mireille Bousquet-Mélou,et al.  The generating function of convex polyominoes: The resolution of a q-differential system , 1995, Discret. Math..

[4]  D. Klarner Cell Growth Problems , 1967, Canadian Journal of Mathematics.

[5]  D. Hugh Redelmeier,et al.  Counting polyominoes: Yet another attack , 1981, Discret. Math..

[6]  Günter Rote,et al.  Λ > 4: an Improved Lower Bound on the Growth Constant of Polyominoes , 2016, Commun. ACM.

[7]  Iwan Jensen,et al.  Counting Polyominoes: A Parallel Implementation for Cluster Computing , 2003, International Conference on Computational Science.

[8]  Marie-Pierre Delest,et al.  Generating functions for column-convex polyominoes , 1988, J. Comb. Theory, Ser. A.

[9]  Desh Ranjan,et al.  Vertex isoperimetric parameter of a Computation Graph , 2012, Int. J. Found. Comput. Sci..

[10]  Nándor Sieben Polyominoes with minimum site-perimeter and full set achievement games , 2008, Eur. J. Comb..

[11]  Gill Barequet,et al.  Minimal-Perimeter Polyominoes: Chains, Roots, and Algorithms , 2019, CALDAM.

[12]  Mireille Bousquet-Mélou,et al.  New enumerative results on two-dimensional directed animals , 1998, Discret. Math..

[13]  I. Jensen,et al.  LETTER TO THE EDITOR: Statistics of lattice animals (polyominoes) and polygons , 2000, cond-mat/0007238.

[14]  S. W. Golomb,et al.  Checker Boards and Polyominoes , 1954 .

[15]  Israel A. Wagner,et al.  On Minimal Perimeter Polyminoes , 2006, DGCI.

[16]  D. Klarner,et al.  A Procedure for Improving the Upper Bound for the Number of n-Ominoes , 1972, Canadian Journal of Mathematics - Journal Canadien de Mathematiques.