s-convexity, model sets and their relation
Rings and Algebras
2016-08-15 v1 Mathematical Physics
math.MP
Number Theory
Abstract
The relation of s-convexity and sets modeling physical quasicrystals is explained for quasicrystals related to quadratic unitary Pisot numbers. We show that 1-dimensional model sets may be characterized by s-convexity for finite set of parameters s. It is shown that the three Pisot numbers , , and related to experimentally observed non-crystallographic symmetries are exceptional with respect to s-convexity.
Cite
@article{arxiv.math/9907054,
title = {s-convexity, model sets and their relation},
author = {Zuzana Masáková and Jiří Patera and Edita Pelantová},
journal= {arXiv preprint arXiv:math/9907054},
year = {2016}
}