Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Avoiding two consecutive blocks of same size and same sum over
  $\mathbb{Z}^2$   A long standing question asks whether $\mathbb{Z}$ is uniformly 2-repetitive
[Justin 1972, Pirillo and Varricchio, 1994], that is, whether there is an
infinite sequence over a finite subset of $\mathbb{Z}$ avoiding two consecutive
blocks of same size and same sum or not. Cassaigne \emph{et al.} [2014] showed
that $\mathbb{Z}$ is not uniformly 3-repetitive. We show that $\mathbb{Z}^2$ is
not uniformly 2-repetitive. Moreover, this problem is related to a question
from M\"akel\"a in combinatorics on words and we answer to a weak version of
it.

19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph