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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The hexagonal packing lemma and Rodin Sullivan conjecture


Author: Dov Aharonov
Journal: Trans. Amer. Math. Soc. 343 (1994), 157-167
MSC: Primary 30C85; Secondary 30C62, 52C15
MathSciNet review: 1162100
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Abstract: The Hexagonal Packing Lemma of Rodin and Sullivan [6] states that $ {s_n} \to 0$ as $ n \to \infty $. Rodin and Sullivan conjectured that $ {s_n} = O(1/n)$. This has been proved by Z-Xu He [2]. Earlier, the present author proved the conjecture under some additional restrictions [1].

In the following we are able to remove these restrictions, and thus give an alternative proof of the RS conjecture. The proof is based on our previous article [1]. It is completely different from the proof of He, and it is mainly based on discrete potential theory, as developed by Rodin for the hexagonal case [4].


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1162100-2
PII: S 0002-9947(1994)1162100-2
Article copyright: © Copyright 1994 American Mathematical Society