Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resolving Stanley's conjecture on $k$-fold acyclic complexes   In 1993 Stanley showed that if a simplicial complex is acyclic over some
field, then its face poset can be decomposed into disjoint rank $1$ boolean
intervals whose minimal faces together form a subcomplex. Stanley further
conjectured that complexes with a higher notion of acyclicity could be
decomposed in a similar way using boolean intervals of higher rank. We provide
an explicit counterexample to this conjecture. We also prove a version of the
conjecture for boolean trees and show that the original conjecture holds when
this notion of acyclicity is as high as possible.

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The categories of this paper are: hep-ex
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: quant-ph