Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The structure of maximal zero-sum free Sequences   Let n be an integer, and consider finite sequences of elements of the group
Z/nZ x Z/nZ. Such a sequence is called zero-sum free, if no subsequence has sum
zero. It is known that the maximal length of such a zero-sum free sequence is
2n-2, and Gao and Geroldinger conjectured that every zero-sum free sequence of
this length contains an element with multiplicity at least n-2. By recent
results of Gao, Geroldinger and Grynkiewicz, it essentially suffices to verify
the conjecture for n prime. Now fix a sequence (a_i) of length 2n-2 with
maximal multiplicity of elements at most n-3. There are different approeaches
to show that (a_i) contains a zero-sum; some work well when (a_i) does contain
elements with high multiplicity, others work well when all multiplicities are
small. The aim of this article is to initiate a systematic approach to property
B via the highest occurring multiplicities. Our main results are the following:
denote by m_1 >= m_2 the two maximal multiplicities of (a_i), and suppose that
n is sufficiently big and prime. Then (a_i) contains a zero-sum in any of the
following cases: when m_2 >= 2/3n, when m_1 > (1-c)n, and when m_2 < cn, for
some constant c > 0 not depending on anything.

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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci