Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Numbers of Tuples of Nilpotent Matrices over Finite Fields under
  Simultaneous Conjugation   The problem of classifying tuples of nilpotent matrices over a field under
simultaneous conjugation is considered "hopeless". However, for any given
matrix order over a finite field, the number of concerned orbits is always
finite. This paper gives a closed formula for the number of absolutely
indecomposable orbits using the same methodology as Hua [5]; those orbits are
non-splittable over field extensions. As a consequence, those numbers are
always polynomials in the cardinality of the base field with integral
coefficients. It is conjectured that those coefficients are always
non-negative.

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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph