Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Directional dynamics of $\mathbb{Z}_+\times \mathbb{Z}$-actions
  generated by 1D-CA and the shift map   In this short paper, we compute the directional sequence entropy for of
$\mathbb{Z}_+\times \mathbb{Z}$-actions generated by cellular automata and the
shift map. Meanwhile, we study the directional dynamics of this system. As a
corollary, we prove that there exists a sequence such that for any direction,
some of the systems above have positive directional sequence entropy. Moreover,
with help of mean ergodic theory for directional weak mixing systems, we obtain
a result of number theory about combinatorial numbers.

34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex