Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long $n$-zero-free sequences in finite cyclic groups   A sequence in the additive group ${\mathbb Z}_n$ of integers modulo $n$ is
called $n$-zero-free if it does not contain subsequences with length $n$ and
sum zero. The article characterizes the $n$-zero-free sequences in ${\mathbb
Z}_n$ of length greater than $3n/2-1$. The structure of these sequences is
completely determined, which generalizes a number of previously known facts.
The characterization cannot be extended in the same form to shorter sequence
lengths. Consequences of the main result are best possible lower bounds for the
maximum multiplicity of a term in an $n$-zero-free sequence of any given length
greater than $3n/2-1$ in ${\mathbb Z}_n$, and also for the combined
multiplicity of the two most repeated terms. Yet another application is finding
the values in a certain range of a function related to the classic theorem of
Erd\H{o}s, Ginzburg and Ziv.

5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an