Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On non-repetitive sequences of arithmetic progressions:the cases $k \in
  \{4,5,6,7,8\}$   A $d$-subsequence of a sequence $\varphi = x_1\dots x_n$ is a subsequence
$x_i x_{i+d} x_{i+2d} \dots$, for any positive integer $d$ and any $i$, $1 \le
i \le n$. A \textit{$k$-Thue sequence} is a sequence in which every
$d$-subsequence, for $1 \le d \le k$, is non-repetitive, i.e. it contains no
consecutive equal subsequences. In 2002, Grytczuk proposed a conjecture that
for any $k$, $k+2$ symbols are enough to construct a $k$-Thue sequences of
arbitrary lengths. So far, the conjecture has been confirmed for $k \in
\{1,2,3,5\}$. Here, we present two different proving techniques, and confirm it
for all $k$, with $2 \le k \le 8$.

22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph