Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approaches for enumerating permutations with a prescribed number of
  occurrences of patterns   In recent work, Zeilberger and the author used a functional equations
approach for enumerating permutations with r occurrences of the pattern 12...k.
In particular, the approach yielded a polynomial-time enumeration algorithm for
any fixed nonnegative r. We extend that approach to patterns of the form
12...(k-2)(k)(k-1) by deriving analogous functional equations and using them to
develop similar algorithms that enumerate permutations with r occurrences of
the pattern. We also generalize those techniques to handle patterns of the form
23...k1 and derive analogous functional equations and enumeration algorithms.
Finally, we show how the functional equations and algorithms can be modified to
track inversions as well as handle multiple patterns simultaneously. This paper
is accompanied by Maple packages that implement the algorithms described.

1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg