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On the Wildness of Cambrian Lattices [PDF]
Algebras and Representation Theory, 2018 In this note, we investigate the representation type of the cambrian lattices and some other related lattices. The result is expressed as a very simple trichotomy. When the rank of the underlined Coxeter group is at most 2, the lattices are of finite representation type.
Chapoton, Frédéric, Rognerud, Baptiste
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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.
Nathan Reading
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Towards m-Cambrian Lattices [PDF]
, 2013 20 pages, 13 figures.
Kallipoliti, Myrto, Mühle, Henri
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Electron. Notes Discret. Math., 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
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An analogue of distributivity for ungraded lattices [PDF]
Order, 2005 In this paper, we define a property, trimness, for lattices. Trimness is a not-necessarily-graded generalization of distributivity; in particular, if a lattice is trim and graded, it is distributive.
Thomas, Hugh
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The Cambrian Hopf Algebra [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Cambrian trees are oriented and labeled trees which fulfill local conditions around each node generalizing the conditions for classical binary search trees.
G. Chatel, V. Pilaud
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Generalized associahedra via brick polytopes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We generalize the brick polytope of V. Pilaud and F. Santos to spherical subword complexes for finite Coxeter groups. This construction provides polytopal realizations for a certain class of subword complexes containing all cluster complexes of finite ...
Vincent Pilaud, Christian Stump
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EL-labelings and canonical spanning trees for subword complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We describe edge labelings of the increasing flip graph of a subword complex on a finite Coxeter group, and study applications thereof. On the one hand, we show that they provide canonical spanning trees of the facet-ridge graph of the subword complex ...
Vincent Pilaud, Christian Stump
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Pop-Stack Operators for Torsion Classes and Cambrian Lattices
, 2023 50 pages, 7 ...
Barnard, Emily +2 more
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On the Topology of the Cambrian Semilattices [PDF]
, 2012 For an arbitrary Coxeter group $W$, David Speyer and Nathan Reading defined Cambrian semilattices $C_{\gamma}$ as semilattice quotients of the weak order on $W$ induced by certain semilattice homomorphisms.
Kallipoliti, Myrto, Mühle, Henri
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