Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Character-theoretic Techniques for Near-central Enumerative Problems   The centre of the symmetric group algebra $\mathbb{C}[\mathfrak{S}_n]$ has
been used successfully for studying important problems in enumerative
combinatorics. These include maps in orientable surfaces and ramified covers of
the sphere by curves of genus $g$, for example. However, the combinatorics of
some equally important $\mathfrak{S}_n$-factorization problems forces $k$
elements in $\{1,...,n\}$ to be distinguished. Examples of such problems
include the star factorization problem, for which $k=1,$ and the enumeration of
2-cell embeddings of dipoles with two distinguished edges
\cite{VisentinWieler:2007} associated with Berenstein-Maldacena-Nastase
operators in Yang-Mills theory \cite{ConstableFreedmanHeadrick:2002}, for which
$k=2.$ Although distinguishing these elements obstructs the use of central
methods, these problems may be encoded algebraically in the centralizer of
$\mathbb{C}[\mathfrak{S}_n]$ with respect to the subgroup $\mathfrak{S}_{n-k}.$
We develop methods for studying these problems for $k=1,$ and demonstrate their
efficacy on the star factorization problem. In a subsequent paper
\cite{JacksonSloss:2011}, we consider a special case of the the above dipole
problem by means of these techniques.

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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: physics