Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of sublattice points in lattice polygons   We state the formula for the critical number of vertices of a convex lattice
polygon that guarantees that the polygon contains at least one point of a given
sublattice and give a partial proof of the formula. We show that the proof can
be reduced to finding upper bounds on the number of vertices in certain classes
of polygons. To obtain these bounds, we establish inequalities relating the
number of edges of a broken line and the coordinates of its endpoints within a
suitable class of broken lines.

8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin