Compact packings of the plane with three sizes of discs

Autor:	Fernique, Thomas, Hashemi, Amir, Sizova, Olga
Rok vydání:	2018
Předmět:	Computer Science - Discrete Mathematics Mathematics - Combinatorics 05B40 52C15 52C26 11H31 65D18 68W30 68U05
Druh dokumentu:	Working Paper
DOI:	10.1007/s00454-019-00166-y
Popis:	A compact packing is a set of non-overlapping discs where all the holes between discs are curvilinear triangles. There is only one compact packing by discs of size $1$. There are exactly $9$ values of $r$ which allow a compact packing by discs of sizes $1$ and $r$. We prove here that there are exactly $164$ pairs $(r,s)$ allowing a compact packing by discs of sizes $1$, $r$ and $s$. Comment: code (SageMath) included
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1810.02231 Zobrazit plný text záznamu View this record from Arxiv