Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Applying Computer Algebra Systems with SAT Solvers to the Williamson
  Conjecture   We employ tools from the fields of symbolic computation and satisfiability
checking---namely, computer algebra systems and SAT solvers---to study the
Williamson conjecture from combinatorial design theory and increase the bounds
to which Williamson matrices have been enumerated. In particular, we completely
enumerate all Williamson matrices of even order up to and including 70 which
gives us deeper insight into the behaviour and distribution of Williamson
matrices. We find that, in contrast to the case when the order is odd,
Williamson matrices of even order are quite plentiful and exist in every even
order up to and including 70. As a consequence of this and a new construction
for 8-Williamson matrices we construct 8-Williamson matrices in all odd orders
up to and including 35. We additionally enumerate all Williamson matrices whose
orders are divisible by 3 and less than 70, finding one previously unknown set
of Williamson matrices of order 63.

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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg