Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sylvan resolutions in three variables   The canonical sylvan resolution is a resolution for arbitrary monomial ideals
over a polynomial ring that is minimal and has an explicit combinatorial
formula for the differential. The differential is a weighted sum over lattice
paths of weights of chain-link fences, which are sequences of faces that are
linked to each other via higher-dimensional analogues of spanning trees. The
combinatorial formula for the differential simplifies greatly in the
three-variable case. The main results in this paper express the sylvan matrix
entries for monomial ideals in three variables as a sum over lattice paths of
simpler weights that depend only on the number of specific Koszul simplicial
complexes that lie along the corresponding lattice path, which bypasses any
computation of chain-link fences.

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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-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: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: hep-th