Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A refinement of the binomial distribution using the quantum binomial
  theorem   $q$-analogs of special functions, including hypergeometric functions, play a
central role in mathematics and have numerous applications in physics. In the
theory of probability, $q$-analogs of various probability distributions have
been introduced over the years, including the binomial distribution. Here, I
propose a new refinement of the binomial distribution by way of the quantum
binomial theorem (also known as the the noncommutative $q$-binomial theorem),
where the $q$ is a formal variable in which information related to the sequence
of successes and failures in the underlying binomial experiment is encoded in
its exponent.

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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol