Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the spectra of Pisot-cyclotomic numbers   We investigate the complex spectra \[ X^{\mathcal
A}(\beta)=\left\{\sum_{j=0}^na_j\beta^j : n\in{\mathbb N},\ a_j\in{\mathcal
A}\right\} \] where $\beta$ is a quadratic or cubic Pisot-cyclotomic number and
the alphabet $\mathcal A$ is given by $0$ along with a finite collection of
roots of unity. Such spectra are discrete aperiodic structures with
crystallographically forbidden symmetries. We discuss in general terms under
which conditions they possess the Delone property required for point sets
modeling quasicrystals. We study the corresponding Voronoi tilings and we
relate these structures to quasilattices arising from the cut and project
method.

26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th