Lattice and order properties of the poset of regions in a hyperplane arrangement

53 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Sortable elements and Cambrian lattices (2005, unknown): “( In some earlier papers [16, 17] where shards were considered, closures were not taken.)”
Lattice Properties of Oriented Exchange Graphs and Torsion Classes (2015, background): “Congruence-uniform lattices admit other characterizations in terms of lattice congruences [14], edge-labelings [25], or as “bounded” quotients of free lattices.”
Sortable elements in infinite Coxeter groups (2008, background): “f free lattices and by Proposition 2.12, that every interval in the weak order is a semidistributive lattice in the sense of [19, Section I.3]. A stronger result was proven, for W ﬁnite, in [11]. Cf. [10, 28]. More importantly in for our purposes, canonical join representations of sortable elements ”
Noncrossing partitions and the shard intersection order (2009, unknown): “The lattice (W, ) is defined in terms of the polyhedral geometry of shards, certain codimension-1 cones introduced and studied in [27, 28, 30, 34].”