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arxiv: 1906.08447 · v3 · pith:GTQKZZHW · submitted 2019-06-20 · math.CO · math-ph· math.AT· math.MP

Polyiamonds Attaining Extremal Topological Properties, Part II

Greg Malen , \'Erika Rold\'an This is my paper

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classification math.CO math-phmath.ATmath.MP
keywords polyiamondscrystallizedholeseverypartattainingconditionsconstruct
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In Part II of this work, we construct crystallized polyiamonds with $h$ holes for every $h\ge1$, that is polyiamonds which use the fewest possible tiles necessary to enclose $h$ holes. Furthermore, we prove that crystallized polyiamonds satisfy a set of structural conditions, and for every $h\ge 3$ there are multiple distinct crystallized polyiamonds with $h$ holes.

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