Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 132-avoiding Two-stack Sortable Permutations, Fibonacci Numbers, and
  Pell Numbers   In 1990 West conjectured that there are $2(3n)!/((n+1)!(2n+1)!)$ two-stack
sortable permutations on $n$ letters. This conjecture was proved analytically
by Zeilberger in 1992. Later, Dulucq, Gire, and Guibert gave a combinatorial
proof of this conjecture. In the present paper we study generating functions
for the number of two-stack sortable permutations on $n$ letters avoiding (or
containing exactly once) 132 and avoiding (or containing exactly once) an
arbitrary permutation $\tau$ on $k$ letters. In several interesting cases this
generating function can be expressed in terms of the generating function for
the Fibonacci numbers or the generating function for the Pell numbers.

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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: gr-qc