On the lattice property of shard orders

zbMath1465.06003MaRDI QIDQ2632682

Mühle Henri

Publication date: 15 May 2019

Published in: Séminaire Lotharingien de Combinatoire (Search for Journal in Brave)

Full work available at URL: http://www.mat.univie.ac.at/~slc/wpapers/FPSAC2018//04-Muehle.html

zbMATH Keywords

Möbius functionbiclosed setssemidistributive latticescongruence-uniform latticescrosscut theoreminterval doubling

Mathematics Subject Classification ID

Combinatorics of partially ordered sets (06A07) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Structure theory of lattices (06B05) Other generalizations of distributive lattices (06D75)

Related Items (1)

The canonical join complex for biclosed sets

Uses Software

• SageMath
• Sage-Combinat

Cites Work

• Unnamed Item
• Noncrossing partitions and the shard intersection order
• The canonical join complex
• Oriented flip graphs of polygonal subdivisions and noncrossing tree partitions
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• The order dimension of the poset of regions in a hyperplane arrangement.
• Crosscut-simplicial lattices
• Lattice and order properties of the poset of regions in a hyperplane arrangement
• Lattice Theory of the Poset of Regions
• Lattice Theory: Foundation
• A Partial Order on the Regions of R n Dissected by Hyperplanes
• Clusters, Coxeter-sortable elements and noncrossing partitions
• Characterizations of Finite Lattices that are Bounded-Homomqrphic Images or Sublattices of Free Lattices
• Noncrossing Arc Diagrams and Canonical Join Representations
• On the Shard Intersection Order of a Coxeter Group
• Equational Bases and Nonmodular Lattice Varieties
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]
• On the distributivity of a lattice of lattice-congruences

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