Results 21 to 30 of about 1,075 (101)
Sortable elements and Cambrian lattices [PDF]
Algebra universalis, 2007 We show that the Coxeter-sortable elements in a finite Coxeter group W are the minimal congruence-class representatives of a lattice congruence of the weak order on W. We identify this congruence as the Cambrian congruence on W, so that the Cambrian lattice is the weak order on Coxeter-sortable elements.
openaire +2 more sources
The facial weak order and its lattice quotients [PDF]
, 2016 We investigate a poset structure that extends the weak order on a finite Coxeter group $W$ to the set of all faces of the permutahedron of $W$. We call this order the facial weak order.
Dermenjian, Aram +2 more
core +4 more sources
Lattice theory of torsion classes [PDF]
, 2018 The aim of this paper is to establish a lattice theoretical framework to study the partially ordered set $\operatorname{\mathsf{tors}} A$ of torsion classes over a finite-dimensional algebra $A$.
Demonet, Laurent +4 more
core +2 more sources
The extended permutohedron on a transitive binary relation [PDF]
, 2013 For a given transitive binary relation e on a set E, the transitive closures of open (i.e., co-transitive in e) sets, called the regular closed subsets, form an ortholattice Reg(e), the extended permutohedron on e.
Santocanale, Luigi, Wehrung, Friedrich
core +4 more sources
Lattice congruences of the weak order [PDF]
, 2004 We study the congruence lattice of the poset of regions of a hyperplane arrangement, with particular emphasis on the weak order on a finite Coxeter group.
A. Björner +17 more
core +2 more sources
, 2017 We introduce permutrees, a unified model for permutations, binary trees, Cambrian trees and binary sequences. On the combinatorial side, we study the rotation lattices on permutrees and their lattice homomorphisms, unifying the weak order, Tamari ...
Pilaud, Vincent, Pons, Viviane
core +6 more sources
Noncrossing partitions and representations of quivers [PDF]
, 2008 We situate the noncrossing partitions associated to a finite Coxeter group within the context of the representation theory of quivers. We describe Reading's bijection between noncrossing partitions and clusters in this context, and show that it extends ...
Assem +12 more
core +3 more sources
From the Tamari Lattice to Cambrian Lattices and Beyond [PDF]
, 2012 In this chapter, we trace the path from the Tamari lattice, via lattice congruences of the weak order, to the definition of Cambrian lattices in the context of finite Coxeter groups, and onward to the construction of Cambrian fans. We then present sortable elements, the key combinatorial tool for studying Cambrian lattices and fans.
openaire +2 more sources
Geometric realizations of the accordion complex of a dissection [PDF]
, 2018 Consider $2n$ points on the unit circle and a reference dissection $\mathrm{D}_\circ$ of the convex hull of the odd points. The accordion complex of $\mathrm{D}_\circ$ is the simplicial complex of non-crossing subsets of the diagonals with even endpoints
Manneville, Thibault, Pilaud, Vincent
core +4 more sources
Noncrossing partitions and the shard intersection order [PDF]
, 2009 We define a new lattice structure on the elements of a finite Coxeter group W. This lattice, called the shard intersection order, is weaker than the weak order and has the noncrossing partition lattice NC(W) as a sublattice. The new construction of NC(W)
Reading, Nathan
core +5 more sources