155 citations · 1.3k across the 42 of their papers we have counts for
42 papers
Noncrossing partitions of an annulus
Laura G. Brestensky, Nathan Reading
The noncrossing partition poset associated to a Coxeter group and Coxeter element is the interval in the absolute order on . We construct a new model of noncro…
Noncrossing partitions of a marked surface
Nathan Reading
We define noncrossing partitions of a marked surface without punctures (interior marked points). We show that the natural partial order on noncrossing partitions is a graded lattic…
Cluster scattering diagrams of acyclic affine type
Nathan Reading, Salvatore Stella
We give an explicit construction of the cluster scattering diagram for any acyclic exchange matrix of affine type. We show that the corresponding cluster scattering fan coincides b…
The fundamental theorem of finite semidistributive lattices
Nathan Reading, David E Speyer, Hugh Thomas
We prove a Fundamental Theorem of Finite Semidistributive Lattices (FTFSDL), modelled on Birkhoff's Fundamental Theorem of Finite Distributive Lattices. Our FTFSDL is of the form "…
The action of a Coxeter element on an affine root system
Nathan Reading, Salvatore Stella
The characterization of orbits of roots under the action of a Coxeter element is a fundamental tool in the study of finite root systems and their reflection groups. This paper deve…
A combinatorial approach to scattering diagrams
Nathan Reading
Scattering diagrams arose in the context of mirror symmetry, but a special class of scattering diagrams (the cluster scattering diagrams) were recently developed to prove key struc…
Dominance phenomena: mutation, scattering and cluster algebras
Nathan Reading
An exchange matrix dominates an exchange matrix if the signs of corresponding entries weakly agree, with the entry of always having weakly greater absolute value. When…
Scattering fans
Nathan Reading
Scattering diagrams arose in the context of mirror symmetry, Donaldson-Thomas theory, and integrable systems. We show that a consistent scattering diagram with minimal support cuts…
Lattice homomorphisms between weak orders
Nathan Reading
We classify surjective lattice homomorphisms between the weak orders on finite Coxeter groups. Equivalently, we classify lattice congruences on such that the quot…
Lattice theory of torsion classes: Beyond -tilting theory
Laurent Demonet, Osamu Iyama, Nathan Reading +2
The aim of this paper is to establish a lattice theoretical framework to study the partially ordered set of torsion classes over a finite-dimension…
An affine almost positive roots model
Nathan Reading, Salvatore Stella
We generalize the almost positive roots model for cluster algebras from finite type to a uniform finite/affine type model. We define the almost positive Schur roots and a com…
A Vizing-like theorem for union vertex-distinguishing edge coloring
Nicolas Bousquet, Antoine Dailly, Eric Duchene +2
We introduce a variant of the vertex-distinguishing edge coloring problem, where each edge is assigned a subset of colors. The label of a vertex is the union of the sets of colors…
Lattice structure of Weyl groups via representation theory of preprojective algebras
Osamu Iyama, Nathan Reading, Idun Reiten +1
This paper studies the combinatorics of lattice congruences of the weak order on a finite Weyl group , using representation theory of the corresponding preprojective algebra …
Universal geometric coefficients for the four-punctured sphere
Emily Barnard, Emily Meehan, Nathan Reading +1
We construct universal geometric coefficients for the cluster algebra associated to the four-punctured sphere and obtain, as a by-product, the g-vectors of cluster variables. We al…
A Cambrian framework for the oriented cycle
Nathan Reading, David E. Speyer
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 c…
Cambrian frameworks for cluster algebras of affine type
Nathan Reading, David E. Speyer
We give a combinatorial model for the exchange graph and g-vector fan associated to any acyclic exchange matrix B of affine type. More specifically, we construct a reflection frame…
Coxeter arrangements in three dimensions
Richard Ehrenborg, Caroline Klivans, Nathan Reading
Let be a finite real linear hyperplane arrangement in three dimensions. Suppose further that all the regions of are isometric. We prove that ${\mathca…
Initial-seed recursions and dualities for d-vectors
Nathan Reading, Salvatore Stella
We present an initial-seed-mutation formula for d-vectors of cluster variables in a cluster algebra. We also give two rephrasings of this recursion: one as a duality formula for d-…
Noncrossing arc diagrams and canonical join representations
Nathan Reading
We consider two problems that appear at first sight to be unrelated. The first problem is to count certain diagrams consisting of noncrossing arcs in the plane. The second problem…
Universal geometric coefficients for the once-punctured torus
Nathan Reading
We construct universal geometric coefficients, over the integers, the rationals, and the reals, for cluster algebras arising from the once-punctured torus. We verify that the once-…
Universal geometric cluster algebras from surfaces
Nathan Reading
A universal geometric cluster algebra over an exchange matrix B is a universal object in the category of geometric cluster algebras over B related by coefficient specializations. (…
Universal geometric cluster algebras
Nathan Reading
We consider, for each exchange matrix B, a category of geometric cluster algebras over B and coefficient specializations between the cluster algebras. The category also depends on…
Combinatorial frameworks for cluster algebras
Nathan Reading, David E Speyer
We develop a general approach to finding combinatorial models for cluster algebras. The approach is to construct a labeled graph called a framework. When a framework is constructed…
From the Tamari lattice to Cambrian lattices and beyond
Nathan Reading
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 group…