Work

Cut and project sets with polytopal window I: Complexity

Year: 2020

Type: article

Abstract: We calculate the growth rate of the complexity function for polytopal cut and project sets. This generalizes work of Julien where the almost canonical condition is assumed. The analysis of polytopal cut and project sets has often relied on being able to replace acceptance domains of patterns by so-called cut regions. Our results correct mistakes in the literature where these two notions are incorrectly identified. One may only relate acceptance domains and cut regions when additional conditions on the cut and project set hold. We find a natural condition, called the quasicanonical condition, guaranteeing this property and demonstrate by counterexample that the almost canonical condition is not sufficient for this. We also discuss the relevance of this condition for the current techniques used to study the algebraic topology of polytopal cut and project sets.

Source: Ergodic Theory and Dynamical Systems

DOI: 10.1017/etds.2020.10

Authors: HENNA KOIVUSALO, JAMES J. WALTON

Institutions: University of Vienna, University of Glasgow

Language: English

Topic: Quasicrystal Structures and Properties

Subfield: Materials Chemistry

Field: Materials Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,160

Funders: London Mathematical Society, Engineering and Physical Sciences Research Council