Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bruck nets and partial Sherk planes   In Bachmann's Aufbau der Geometrie aus dem Spiegelungsbegriff (1959), it was
shown that a finite metric plane is a Desarguesian affine plane of odd order
equipped with a perpendicularity relation on lines, and conversely. Sherk
(1967) generalised this result to characterise the finite affine planes of odd
order by removing the 'three reflections axioms' from a metric plane. We show
that one can obtain a larger class of natural finite geometries, the so-called
Bruck nets of even degree, by weakening Sherk's axioms to allow non-collinear
points.

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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys