Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enumeration of associative magic squares of order 7   An associative magic square is a magic square such that the sum of any 2
cells at symmetric positions with respect to the center is constant. The total
number of associative magic squares of order 7 is enormous, and thus, it is not
realistic to obtain the number by simple backtracking. As a recent result,
Artem Ripatti reported the number of semi-magic squares of order 6 (the magic
squares of 6x6 without diagonal sum conditions) in 2018. In this research, with
reference to Ripatti's method of enumerating semi-magic squares, we have
calculated the total number of associative magic squares of order 7. There are
exactly 1,125,154,039,419,854,784 associative magic squares of order 7,
excluding symmetric patterns.

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The categories of this paper are: mtrl-th
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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: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th