Polyiamonds and Polyhexes with Minimum Site-Perimeter and Achievement Games

Gábor Fülep, Nándor Sieben

Abstract


An animal is an edge connected set of finitely many cells of a regular tiling of the plane. The site-perimeter of an animal is the number of empty cells connected to the animal by an edge. The minimum site-perimeter with a given cell size is found for animals on the triangular and hexagonal grid. The formulas are used to show the effectiveness of a simple random strategy in full set animal achievement games.


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