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arXiv · 2205.11897

Complexity of Cut-and-Project Sets of Polytopal Type in Special Homogeneous Lie Groups

Peter Kaiser
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Abstract

The aim of this paper is to determine the asymptotic growth rate of the complexity function of cut-and-project sets in the non-abelian case. In the case of model sets of polytopal type in homogeneous two-step nilpotent Lie groups we can establish that the complexity function asymptotically behaves like $r^{homdim(G) dim(H)}$. Further we generalize the concept of acceptance domains to locally compact second countable groups.

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Peter Kaiser. 2022-05-24. Complexity of Cut-and-Project Sets of Polytopal Type in Special Homogeneous Lie Groups. https://arxiv.org/abs/2205.11897

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