Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorics of faithfully balanced modules   We study and classify faithfully balanced modules for the algebra of lower
triangular $n$ by $n$ matrices. The theory extends known results about tilting
modules, which are classified by binary trees, and counted with the Catalan
numbers. The number of faithfully balanced modules is a $2$-factorial number.
Among them are $n!$ modules with $n$ indecomposable summands, which can be
classified by interleaved binary trees or by increasing binary trees.

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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom