Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On totally disconnected generalised Sierpinski carpets   Generalised Sierpinski carpets are planar sets that generalise the well-known
Sierpinski carpet and are defined by means of sequences of patterns. We study
the structure of the sets at the kth iteration in the construction of the
generalised carpet, for k greater than or equal to 1. Subsequently, we show
that certain families of patterns provide total disconnectedness of the
resulting generalised carpets. Moreover, analogous results hold even in a more
general setting. Finally, we apply the obtained results in order to give an
example of a totally disconnected generalised carpet with box-counting
dimension 2.

25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat