Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting ternary trees according to the number of middle edges and
  factorizing into $(3/2)$-ary trees   The sequence A120986 in the Encyclopedia of Integer Sequences counts ternary
trees according to the number of nodes and the number of middle edges. Using a
certain substition, the underlying cubic equation can be factored. This leads
to an extension of the concept of $(3/2)$-ary trees, introduced by Knuth in his
christmas lecture from 2014.

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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys