Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Acyclic reorientation lattices and their lattice quotients   We prove that the acyclic reorientation poset of a directed acyclic graph $D$
is a lattice if and only if the transitive reduction of any induced subgraph of
$D$ is a forest. We then show that the acyclic reorientation lattice is always
congruence normal, semidistributive (thus congruence uniform) if and only if
$D$ is filled, and distributive if and only if $D$ is a forest. When the
acyclic reorientation lattice is semidistributive, we introduce the ropes of
$D$ that encode the join irreducibles acyclic reorientations and exploit this
combinatorial model in three directions. First, we describe the canonical join
and meet representations of acyclic reorientations in terms of non-crossing
rope diagrams. Second, we describe the congruences of the acyclic reorientation
lattice in terms of lower ideals of a natural subrope order. Third, we use
Minkowski sums of shard polytopes of ropes to construct a quotientope for any
congruence of the acyclic reorientation lattice.

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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin