Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enumeration of permutations by number of cyclic occurrence of peaks and
  valleys   In this paper, we focus on the enumeration of permutations by number of
cyclic occurrence of peaks and valleys. We find several recurrence relations
involving the number of permutations with a prescribed number of cyclic peaks,
cyclic valleys, fixed points and cycles. Several associated permutation
statistics and the corresponding generating functions are also studied. In
particular, we establish a connection between cyclic valleys and Pell numbers
as well as cyclic peaks and alternating runs.

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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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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: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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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: eess
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol