# name
Acyclic reorientation lattices and their lattice quotients

# metadata.dc.description.abstract[].value
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 semidis-
tributive, we introduce the ropes of D that encode the join irreducible
acyclic reorientations and exploit this combinatorial model in three direc-
tions. 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.

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Acyclic reorientation lattices and their lattice quotients