Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Steiner Triple Systems of Order 21 with Subsystems   The smallest open case for classifying Steiner triple systems is order 21. A
Steiner triple system of order 21, an STS(21), can have subsystems of orders 7
and 9, and it is known that there are 12,661,527,336 isomorphism classes of
STS(21)s with sub-STS(9)s. The classification of STS(21)s with subsystems is
here completed by settling the case of STS(21)s with sub-STS(7)s; there are
116,635,963,205,551 isomorphism classes of such systems. An estimation of the
number of isomorphism classes of STS(21)s is given.

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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
18
The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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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: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph