Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasicrystals: A matter of definition   It is argued that the prevailing definition of quasicrystals, requiring them
to contain an axis of symmetry that is forbidden in periodic crystals, is
inadequate. This definition is too restrictive in that it excludes an important
and interesting collection of structures that exhibit all the well-known
properties of quasicrystals without possessing any forbidden symmetries.

2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex