6,174 research outputs found
On the structure of Ammann A2 tilings
We establish a structure theorem for the family of Ammann A2 tilings of the
plane. Using that theorem we show that every Ammann A2 tiling is self-similar
in the sense of [B. Solomyak, Nonperiodicity implies unique composition for
self-similar translationally finite tilings, Discrete and Computational
Geometry 20 (1998) 265-279]. By the same techniques we show that Ammann A2
tilings are not robust in the sense of [B. Durand, A. Romashchenko, A. Shen.
Fixed-point tile sets and their applications, Journal of Computer and System
Sciences, 78:3 (2012) 731--764]
Finite Simple Groups as Expanders
We prove that there exist and such that every
non-abelian finite simple group , which is not a Suzuki group, has a set of
generators for which the Cayley graph \Cay(G; S) is an
-expander.Comment: 10 page
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