79 citations · 635 across the 51 of their papers we have counts for
61 papers
Signed seeds and G-gradings on cluster algebras
Lauren Williams, Alan Yan
The theory of cluster algebras is closely connected to the theory of total positivity; indeed, the desire to better understand total positivity was one of the main motivations for…
Polyhedral and Tropical Geometry of Flag Positroids
Jonathan Boretsky, Christopher Eur, Lauren Williams
A flag positroid of ranks on is a flag matroid that can be realized by a real matrix such that the mino…
Grass trees and forests: Enumeration of Grassmannian trees and forests, with applications to the momentum amplituhedron
Robert Moerman, Lauren K. Williams
The Exponential Formula allows one to enumerate any class of combinatorial objects built by choosing a set of connected components and placing a structure on each connected compone…
The positive Grassmannian, the amplituhedron, and cluster algebras
Lauren K. Williams
The positive Grassmannian is the subset of the real Grassmannian where all Plücker coordinates are nonnegative. It has a beautiful combinatorial structure as we…
Schubert polynomials, the inhomogeneous TASEP, and evil-avoiding permutations
Donghyun Kim, Lauren Williams
Consider a lattice of n sites arranged around a ring, with the sites occupied by particles of weights ; the possible arrangements of particles in sites thus co…
The m=2 amplituhedron and the hypersimplex: signs, clusters, triangulations, Eulerian numbers
Matteo Parisi, Melissa Sherman-Bennett, Lauren Williams
The hypersimplex is the image of the positive Grassmannian under the moment map. It is a polytope of dimension in . Meanwhile,…