Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diagonal Solutions to the 2-Toda Hierarchy   Using a combinatorial description of the Bernstein operator and its action on
Schur functions, we describe the formal power series solutions to a family of
partial differential equations known as the 2-Toda hierarchy. We also
characterize diagonal solutions and use this to prove that a special family of
formal power series, called content-type series, are solutions to the 2-Toda
hierarchy. As examples, we prove that various generating series for permutation
factorization problems (including the double Hurwitz problem), correlators for
the Schur measure on partitions and the formal character expansion of the HCIZ
integral are all solutions to the 2-Toda hierarchy.

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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: econ