Advances in Mathematics, 2006 Revisions in exposition (partly in response to the suggestions of an anonymous referee) including many new figures. Also, Conjecture 1.4 and Theorem 1.5 are replaced by slightly more detailed statements. To appear in Adv. Math.
Nathan Reading
openaire +4 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.
Nathan Reading
openaire +3 more sources
Lattice Properties of Oriented Exchange Graphs and Torsion Classes [PDF]
Algebras and Representation Theory, 2018 The exchange graph of a 2-acyclic quiver is the graph of mutation-equivalent quivers whose edges correspond to mutations. When the quiver admits a nondegenerate Jacobi-finite potential, the exchange graph admits a natural acyclic orientation called the ...
Garver, Alexander, McConville, Thomas
core +3 more sources
Cambrian triangulations and their tropical realizations [PDF]
European journal of combinatorics (Print), 2018 This paper develops a Cambrian extension of the work of C. Ceballos, A. Padrol and C. Sarmiento on $\nu$-Tamari lattices and their tropical realizations.
Pilaud, Vincent
core +2 more sources
Realizations of the associahedron and cyclohedron [PDF]
Discrete & Computational Geometry, 2005 We describe many different realizations with integer coordinates for the associahedron (i.e. the Stasheff polytope) and for the cyclohedron (i.e. the Bott-Taubes polytope) and compare them to the permutahedron of type A_n and B_n respectively.
Hohlweg, Christophe, Lange, Carsten
core +5 more sources
Structure and function of a compound eye, more than half a billion years old. [PDF]
Proc Natl Acad Sci U S A, 2017 Significance An exceptionally well-preserved arthropod fossil from near the base of the lower Cambrian shows the internal sensory structures of a compound eye, more than half a billion years old. The trilobite to which it belongs is found in a zone where
Schoenemann B +2 more
europepmc +2 more sources
Geophysical Monograph Series, Page 487-501., 2021 Exploring the links between Large Igneous Provinces and dramatic environmental impact
An emerging consensus suggests that Large Igneous Provinces (LIPs) and Silicic LIPs (SLIPs) are a significant driver of dramatic global environmental and biological changes, including mass extinctions.
Charles W. Diamond +3 more
wiley +1 more source
A Cambrian Framework for the Oriented Cycle [PDF]
Electronic Journal of Combinatorics, 2015 This paper completes the project of constructing combinatorial models (called frameworks) for the exchange graph and g-vector fan associated to any exchange matrix B whose Cartan companion is of finite or affine type, using the combinatorics and geometry
Nathan Reading, David E. Speyer
semanticscholar +1 more source
Lattice structure of Grid-Tamari orders [PDF]
Journal of Combinatorial Theory, 2015 The Tamari order is a central object in algebraic combinatorics and many other areas. Defined as the transitive closure of an associativity law, the Tamari order possesses a surprisingly rich structure: it is a congruence-uniform lattice.
T. McConville
semanticscholar +1 more source
Lattice Homomorphisms Between Weak Orders [PDF]
Electronic Journal of Combinatorics, 2017 We classify surjective lattice homomorphisms $W\to W'$ between the weak orders on finite Coxeter groups. Equivalently, we classify lattice congruences $\Theta$ on $W$ such that the quotient $W/\Theta$ is isomorphic to $W'$.
Nathan Reading
semanticscholar +1 more source