Polyiamonds Attaining Extremal Topological Properties, Part II

2019/06/20 by Malen, Greg, Roldán, Érika
#05B50 #05Dxx #55N31 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1906.08447

Abstract

In Part II of this work, we construct crystallized polyiamonds with h holes for every h≥1, 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≥ 3 there are multiple distinct crystallized polyiamonds with h holes.

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